Set the length \footskip
to a suitable value, e.g.
\setlength{\footskip}{17pt}
MWE:
\documentclass{article}
\usepackage{fancyhdr}
\renewcommand{\footrulewidth}{0.4pt}
\pagestyle{fancy}
\setlength{\footskip}{17pt}
\begin{document}
AJAX\footnote{Asynchronous JavaScript and XML permet de construire des applications Web et des sites web dynamiques interactifs sur le poste client.}
\end{document}
Output:

EDIT
If you want your footnotes under the foot rule, they will overwrite the page number...
In this case I suggest to delete the line
\renewcommand{\footrulewidth}{0.4pt}
and to redefine \footnoterule
\makeatletter
\renewcommand\footnoterule{%
\kern23\p@
\hrule\@width\linewidth
\kern2.6\p@}
\makeatother
MWE:
\documentclass{article}
\usepackage{fancyhdr}
\usepackage{lipsum} % only for the example
\makeatletter
\renewcommand\footnoterule{%
\kern23\p@
\hrule\@width\linewidth
\kern2.6\p@}
\makeatother
\pagestyle{fancy}
\begin{document}
AJAX\footnote{Asynchronous JavaScript and XML permet de construire des applications Web et des sites web dynamiques interactifs sur le poste client.}
\lipsum[1-8]
\end{document}
