French notation for intervals ]x,y[

you can use \mathopen]x,y\mathclose[

The interval package by Lars Madsen has been designed to take care of this kind of problem (and some others):

\documentclass{article}
\usepackage{interval}
\begin{document}
\[
    \interval[open]{x}{y} \cup \interval[open]{a}{b}
\]
\end{document}

See its documentation for more information.

If you have many of these intervals, you may want to create a dedicated macro called, say, \frint (short for "French-notation interval"...), as follows:

\documentclass{article}
\usepackage{mathtools} % for "\DeclarePairedDelimiter" macro
\DeclarePairedDelimiter{\frint}{]}{[}

\begin{document}
$\frint{x,y}\cup\frint{a,b}$
%% same output as '$\mathopen{]}x,y\mathclose{[} \cup \mathopen{]}a,b\mathclose{[}$'
\end{document}

Then, write \frint* to auto-size the "fences", and write \frint[\big], \frint[\Big], \frint[\bigg], or \frint[\Bigg] to enlarge the fences to a specific, fixed size.