Add letter and simple quote in french with \autoref to appendix

Here is a way with hyperref only (no use of cleveref):

\documentclass[french]{article}
\usepackage{babel}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage[colorlinks,allcolors=blue]{hyperref}

\AtBeginDocument{%
  \def\appendixautorefname{l'appendice}%
}

\begin{document}
\dots\ dans \autoref{appendix_demoPobs}.

\dots\ dans l'appendice~\ref{appendix_demoPobs}.

\appendix
\section{D\'emonstration de l'expression}
\label{appendix_demoPobs}
\end{document}

I don't know how to achieve your typesetting purely with hyperref's machinery. However, it's not too difficult with the help of the cleveref package (which your document loads) and its \Cref macro. Note the use of \Crefname in the code below to provide the prefix l' along with Appendice.

% !TEX TS-program = pdflatex
\documentclass[french]{article}
\usepackage{babel}
\usepackage[T1]{fontenc}
\usepackage{lmodern}

\usepackage[colorlinks,allcolors=blue]{hyperref}
\usepackage[nameinlink,noabbrev]{cleveref}
\Crefname{appendix}{l'Appendice}{les Appendices}

\begin{document}
\dots\ dans \autoref{appendix_demoPobs}.

\dots\ dans \Cref{appendix_demoPobs}.

\dots\ dans l'Appendice~\ref{appendix_demoPobs}.

\appendix
\section{D\'emonstration de l'expression}
\label{appendix_demoPobs}
\end{document}