Weird Vertical Spacing of '*' with Fira Code in Listings

Although @UlrikeFischer’s answer solves the OP, it is still worth mentioning that there are hidden traps. Consider the following “enhanced” example from the OP:

\documentclass{scrartcl}
\usepackage{fontspec,xcolor,listings}
\newfontfamily\firaseries{Fira Code}
\lstdefinestyle{LeonStyle}{
  language=C++,
  basicstyle=\footnotesize\firaseries,
  commentstyle=\color{red}
}
\lstset{style=LeonStyle}
\begin{document}
\begin{lstlisting}
Listing text with *.
C++  a<=b  c=2-1
/* This is a comment. */
This should not be red.
\end{lstlisting}
\end{document}

The hyphen-minus symbol is wrong, too. In fact, it is replaced with a math mode minus $-$ by the listings package.

---

The easiest solution

Don’t load Fira Code via \newfontfamily. Instead, load the font via \setmonofont and use basicstyle=\ttfamily. This signifies Fira Code as a monospaced typeface and prevents listings from replacing certain symbols.

\documentclass{scrartcl}
\usepackage{fontspec,xcolor,listings}
\setmonofont{Fira Code}
\lstdefinestyle{LeonStyle}{
  language=C++,
  basicstyle=\footnotesize\ttfamily,
  commentstyle=\color{red}
}
\lstset{style=LeonStyle}
\begin{document}
\begin{lstlisting}
Listing text with *.
C++  a<=b  c=2-1
/* This is a comment. */
This should not be red.
\end{lstlisting}
\end{document}

---

More elaborate solution

Over the past few days, I have written a small package lstfiracode (shameless plug). It is mainly designed to utilize the Fira Code programming ligatures in the lstlisting environment. If you are using Fira Code, then you probably want the ligatures (otherwise you could just use Fira Mono). Here is how you would implement lstfiracode:

\documentclass{scrartcl}
\usepackage{fontspec,xcolor,listings}
\usepackage{lstfiracode} % https://ctan.org/pkg/lstfiracode
\setmonofont{Fira Code}[Ligatures=Common,Contextuals=Alternate]
\lstset{
  language=C++,
  style=FiraCodeStyle,
  basicstyle=\footnotesize\ttfamily,
  commentstyle=\color{red}
}
\begin{document}
\begin{lstlisting}
Listing text with *.
C++  a<=b  c=2-1
/* This is a comment. */
This should not be red.
\end{lstlisting}
\end{document}

The lstfiracode package is now on CTAN (2018/12/17). It will be available on all the mirrors and the major TeX distributions in the next few days. Enjoy! :)

You can raise the asterix like this:

\documentclass{scrartcl}

\usepackage{fontspec}
\usepackage{xcolor}
\usepackage{listings}

\newfontfamily{\firaseries}{Fira Code}

\lstdefinestyle{mStyle}{
    language=C++,
    basicstyle=\footnotesize\firaseries,
    commentstyle=\color{red}
}

\lstset{style=mStyle}
\makeatletter
\lst@CCPutMacro
    \lst@ProcessOther {"2A}{%
      \lst@ttfamily
         {*}% used with ttfamily
         {\raisebox{1ex}{\textasteriskcentered}}}% used with other fonts
    \@empty\z@\@empty
\makeatother

\begin{document}
    Default font text with *.

    \firaseries This is text in Fira Code with *.

    \begin{lstlisting}
        Listing text with *.
        /* This is a comment. */
        This should not be red.
    \end{lstlisting}
\end{document}

Something like this would work too (or you combine it with a \raisebox):

\makeatletter
\lst@CCPutMacro
    \lst@ProcessOther {"2A}{%
      \lst@ttfamily
         {*}% used with ttfamily
         {*}}% used with other fonts
    \@empty\z@\@empty
\makeatother