The Wikipedia article on alphamagic squares, quoting The Universal Book of Mathematics, says
French allows just one 3 × 3 alphamagic square involving numbers up to 200, but a further 255 squares if the size of the entries is increased to 300.
My script did not find a French alphamagic with entries no larger than 200, but it did find 254 squares with entries no larger than 300. (For each of these squares there are 7 more variations you can form by rotation and reflection.)
The French alphamagic square with the smallest maximum entry that I found is the following.
When spelled out in French we get
And when we replace each cell with its number of letters we get the following magic square:
A list of all the French magic squares with maximum element 300 that I found is available here.