The Unicode symbol for ₣ is:
U+20A3 FRENCH FRANC SIGN
Libertine is an example for a Unicode font that supports the character:
% lualatex or xelatex
\documentclass{article}
\usepackage{libertineotf}
\begin{document}
^^^^20a3 % ASCII notation
\end{document}

Example for GNU FreeFont:
\documentclass{article}
\usepackage{fontspec}
\begin{document}
\fontspec{FreeSerif.otf}
^^^^20a3
\end{document}

Another example for Times New Roman (from Windows 7):
\documentclass{article}
\usepackage{fontspec}
\begin{document}
\fontspec{times.ttf}
^^^^20a3
\end{document}

\fontspec{Comfortaa-Regular.ttf}% Comfortaa Regular:

\fontspec{OpenSans-Regular.ttf}% Open Sans Regular:

Example for siunitx and pdfLaTeX
If lualatex or pdflatex cannot be used, then the symbol can be included as graphics. The graphics is generated by:
% franc.tex
\nofiles
\documentclass{article}
\usepackage{fontspec}
\begin{document}
\fontspec{FreeSerif.otf}
^^^^20a3
\end{document}
It is compiled via:
$ lualatex franc
$ pdfcrop franc
Then franc-crop.pdf can be used as image for pdfLaTeX:
\documentclass{article}
\usepackage{graphicx}
\usepackage{siunitx}
\DeclareRobustCommand*{\myfranc}{\includegraphics[scale=.1]{franc}}
\DeclareSIUnit{\franc}{\myfranc}
\begin{document}
\SI{123.45}{\franc}
\end{document}

If you are using lualatex or xelatex, then the font can be used directly, e.g.:
\DeclareRobustCommand*{\myfranc}{%
\begingroup
\fontspec{FreeSerif.otf}%
^^^^20a3%
\endgroup
}
\normalfontis still Latin Modern (set at\begin{documnet}), this font does not contain the symbol. See my updated answer. – Heiko Oberdiek Mar 19 at 11:43