How to have two optional parameters in a tcolorbox?

A slight variation of the OP's self answer, shifting the 2nd optional argument to the end of the argument list, i.e. it will become the 3rd. argument and transforming the o - type of the first argument to O.

A syntax of \foo[A][B]{...} is bad design and difficult to handle by TeX/LaTeX, since it cannot decide what

\foo[A]{}

is supposed to be. Is A the first optional or the second optional argument? This is unclear.

The o - type specifier from xparse gives a way to decide whether the 1st or the 2nd opt. argument is omitted, but alas, it does not allow for default arguments.

\foo[A]{...}[B] however is clearly recognizable and TeX can distinguish between #1 (being A here) and #3 (being B), so \foo[A]{...}and\foo{...}[B]` is well-defined

\documentclass{article}
\usepackage{lipsum}
\usepackage{xfrac}
\usepackage[most]{tcolorbox}


\NewDocumentCommand{\currentschoolyear}{+O{\the\year}}{%
  \ifnum#1=\the\year%
  \ifnum\month<9%
  \sfrac{\the\numexpr#1-1}{#1}%     #1=2018 --> 2017/2018
  \else
  \sfrac{#1}{\the\numexpr#1+1}%      #1=2018 --> 2018/2019
  \fi
  \else
  \sfrac{#1}{\the\numexpr#1+1}%      
  \fi
}


% For checking reasons only...
%\year=2017
%\month=6

%%%%%%%%%%%%%%%%%%%%%%%%%%%
% boîte resumé

\def\couleurresume{red}%

%% style du titre « résumé du cours »
%\tcbset{titreresume/.style={
%    boxed title style={
%        colframe=#2!50,%
%        colback=#2!10,%
%        coltext=blue,%
%    leftrule=1.5mm,rightrule=1.5mm,toprule=1.5pt,bottom=0pt,boxsep=1pt}}
%}
%
%% style des soustitres des résumés
%\tcbset{soustitre/.style={
%    subtitle style={%
%    colback=#2!7,%
%    colframe=#2!50,%
%    boxsep=1mm,
%    fontupper={\sffamily\bfseries\large\selectfont\color{#2!63!black}}}}
%}

% boîte créant la boîte résumé
\NewTColorBox[auto counter]{resume}{+O{\the\year}+m+O{red}}{%
    minipage boxed title*=-106mm,
    attach boxed title to top center={yshift=-3mm,xshift=-\linewidth/5},
    enhanced,
    nobeforeafter,
    lower separated=false,
%    IfValueTF={#1}{%
    before upper={\textcolor{#3!63!black}{\currentschoolyear[#1] \hfill{#2}\hfill\thetcbcounter/\ref{nombre-de-resume}}},
    % }{%
    %   before upper={\textcolor{#2!63!black}{\currentschoolyear \hfill{#2}\hfill\thetcbcounter/\ref{nombre-de-resume}}},
    % },
    colframe=#3!50,%
    colback=white,%
    coltitle=#3!63!black,%
    leftrule=3mm,rightrule=3mm,
    toprule=2pt,bottomrule=2pt,
    left=3pt,right=0pt,top=3mm,
    fonttitle=\sffamily\bfseries\large,
%    titreresume,
    boxed title style={
        colframe=#3!50,%
        colback=#3!10,%
        coltext=blue,%
    leftrule=1.5mm,rightrule=1.5mm,toprule=1.5pt,bottom=0pt,boxsep=1pt},
%    soustitre,
    subtitle style={%
    colback=#3!7,%
    colframe=#3!50,%
    boxsep=1mm,
    fontupper={\sffamily\bfseries\large\selectfont\color{#3!63!black}}},
    title={\normalsize Résumé}
}

\usepackage{atveryend}
\makeatletter
\AfterLastShipout{%
  \immediate\write\@auxout
  {\string\newlabel{nombre-de-resume}{{\thetcb@cnt@resume}{}}}%
}
\makeatother
\begin{document}

% No optional arguments -> defaults to current year and red
\begin{resume}{chapitre 1}
  \tcbsubtitle{Définition}
  \lipsum[1]
\end{resume}


% both optional arguments -> 2016/2017 and blue
\begin{resume}[2016]{chapitre 1}[blue]
\tcbsubtitle{Définition}

\lipsum[1]
\end{resume}


\newpage

% Only the first optional argument -> 2020 and red
\begin{resume}[2020]{chapitre 1}

\tcbsubtitle{Propriétés}
\lipsum[2]
\end{resume}

% Only the second optional argument  -> current year and green
\begin{resume}{chapitre 1}[green]

\tcbsubtitle{Propriétés}
\lipsum[2]
\end{resume}




%\show\tcbcounter
\end{document}

I just found, just put each optional argument in square brackets.

\begin{resume}[2018][blue]{chapitre 1}

---

I have not yet managed to make sure that I can call this box by indicating only the color (without giving the school year).

Code:

\documentclass{article}
\usepackage{lipsum}
\usepackage{xfrac}
\usepackage[most]{tcolorbox}

\NewDocumentCommand{\currentschoolyear}{+o}{%
  \IfValueTF{#1}{%
    \sfrac{#1}{\the\numexpr#1+1}
  }{%
    \ifnum\month<9%
    \sfrac{\the\numexpr\year-1}{\the\year}%
    \else
    \sfrac{\the\year}{\the\numexpr\year+1}%
    \fi
  }%
}

%\month=7
%\day=31

%%%%%%%%%%%%%%%%%%%%%%%%%%%
% boîte resumé

\def\couleurresume{red}%

%% style du titre « résumé du cours »
%\tcbset{titreresume/.style={
%    boxed title style={
%        colframe=#2!50,%
%        colback=#2!10,%
%        coltext=blue,%
%    leftrule=1.5mm,rightrule=1.5mm,toprule=1.5pt,bottom=0pt,boxsep=1pt}}
%}
%
%% style des soustitres des résumés
%\tcbset{soustitre/.style={
%    subtitle style={%
%    colback=#2!7,%
%    colframe=#2!50,%
%    boxsep=1mm,
%    fontupper={\sffamily\bfseries\large\selectfont\color{#2!63!black}}}}
%}

% boîte créant la boîte résumé
\NewTColorBox[auto counter]{resume}{+o+O{red}+m}{%
    minipage boxed title*=-106mm,
    attach boxed title to top center={yshift=-3mm,xshift=-\linewidth/5},
    enhanced,
    nobeforeafter,
    lower separated=false,
    IfValueTF={#1}{%
      before upper={\textcolor{#2!63!black}{\currentschoolyear[#1] \hfill{#3}\hfill\thetcbcounter/\ref{nombre-de-resume}}},
    }{%
      before upper={\textcolor{#2!63!black}{\currentschoolyear \hfill{#3}\hfill\thetcbcounter/\ref{nombre-de-resume}}},
    },
    colframe=#2!50,%
    colback=white,%
    coltitle=#2!63!black,%
    leftrule=3mm,rightrule=3mm,
    toprule=2pt,bottomrule=2pt,
    left=3pt,right=0pt,top=3mm,
    fonttitle=\sffamily\bfseries\large,
%    titreresume,
    boxed title style={
        colframe=#2!50,%
        colback=#2!10,%
        coltext=blue,%
    leftrule=1.5mm,rightrule=1.5mm,toprule=1.5pt,bottom=0pt,boxsep=1pt},
%    soustitre,
    subtitle style={%
    colback=#2!7,%
    colframe=#2!50,%
    boxsep=1mm,
    fontupper={\sffamily\bfseries\large\selectfont\color{#2!63!black}}},
    title={\normalsize Résumé}
}

\usepackage{atveryend}
\makeatletter
\AfterLastShipout{%
  \immediate\write\@auxout
  {\string\newlabel{nombre-de-resume}{{\thetcb@cnt@resume}{}}}%
}
\makeatother
\begin{document}

\begin{resume}[2017]{chapitre 1}
\tcbsubtitle{Définition}

\lipsum[1]
\end{resume}

\newpage

\begin{resume}[2018][blue]{chapitre 1}

\tcbsubtitle{Propriétés}
\lipsum[2]
\end{resume}

%\show\tcbcounter
\end{document}

What about using different delimiters for the two optional parameters? Like this, for example:

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{xparse}
\NewDocumentCommand\Test{D(){red}O{2018}+m}{%
    Color: #1; Year: #2; mandatory: #3\par
}
\begin{document}
\Test{only mandatory}
\Test(blue){with color}
\Test[2020]{with year}
\Test(green)[1999]{with everything}
\end{document}

which works and, in my opinion, is even easier to remember.

You can combine it with Christian Hupfer's answer to have the current school year (changing the O here to a o).

You can also add a third optional argument with, for example, angle brackets that will be a comma separated string to add to the tcolorbox options.

Applied to your nsMWE:

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{lipsum}
\usepackage{xfrac}
\usepackage[most]{tcolorbox}


\NewDocumentCommand{\currentschoolyear}{+O{\the\year}}{%
  \ifnum\month<9%
  \sfrac{\the\numexpr#1-1}{#1}%     #1=2018 --> 2017/2018
  \else
  \sfrac{#1}{\the\numexpr#1+1}%      #1=2018 --> 2018/2019
  \fi
}

\NewTColorBox[auto counter]{resume}{D<>{}D(){red}O{\the\year}+m}{%
    minipage boxed title*=-106mm,
    attach boxed title to top center={yshift=-3mm,xshift=-\linewidth/5},
    enhanced,
    nobeforeafter,
    lower separated=false,
    before upper={\textcolor{#2!63!black}{\currentschoolyear[#3] \hfill{#4}\hfill\thetcbcounter/\ref{nombre-de-resume}}},
    colframe=#2!50,%
    colback=white,%
    coltitle=#2!63!black,%
    leftrule=3mm,rightrule=3mm,
    toprule=2pt,bottomrule=2pt,
    left=3pt,right=0pt,top=3mm,
    fonttitle=\sffamily\bfseries\large,
%    titreresume,
    boxed title style={
        colframe=#2!50,%
        colback=#2!10,%
        coltext=blue,%
    leftrule=1.5mm,rightrule=1.5mm,toprule=1.5pt,bottom=0pt,boxsep=1pt},
%    soustitre,
    subtitle style={%
    colback=#2!7,%
    colframe=#2!50,%
    boxsep=1mm,
    fontupper={\sffamily\bfseries\large\selectfont\color{#2!63!black}}},
    title={\normalsize Résumé}, 
    #1
}

\usepackage{atveryend}
\makeatletter
\AfterLastShipout{%
  \immediate\write\@auxout
  {\string\newlabel{nombre-de-resume}{{\thetcb@cnt@resume}{}}}%
}
\makeatother
\begin{document}

% No optional arguments -> defaults to current year and red
\begin{resume}{chapitre 1}
  \tcbsubtitle{Définition}
  \lipsum[1]
\end{resume}


% both optional arguments -> 2021 and blue
\begin{resume}(blue)[2021]{chapitre 1}
\tcbsubtitle{Définition}

\lipsum[1]
\end{resume}


\newpage

% Only the first optional argument -> 2020 and red
\begin{resume}[2020]{chapitre 1}

\tcbsubtitle{Propriétés}
\lipsum[2]
\end{resume}

% Only the second optional argument  -> current year and green
\begin{resume}(green){chapitre 1}

\tcbsubtitle{Propriétés}
\lipsum[2]
\end{resume}

%  New optional argument - add whatever to the options to the tcolorbox 
\begin{resume}<colback=red, toprule=1cm>(green){chapitre 1}

\tcbsubtitle{Propriétés}
\lipsum[2]
\end{resume}



%\show\tcbcounter
\end{document}