Thanks AurelBz. Those po/mo files are for Wordpres 3.4.x, and not for the Leaf theme though.
I've just done some more testing.
With Leaf version 1.0 the french translation works much better.
Not for the Search button text but for example "powered by WordPress" gets translated, as well as "More articles" and "Full article".
(Most of the admin "Leaf options" part does not get translated)
I've been trying a few times to manually create a new fr_FR.mo file with poedit, and that failed each time to translate anything at all.
Conclusion : With Leaf version 1.0 the french po/mo worked pretty well
for the webpages but not the small "Leaf options" admin part.
With Leaf version 1.0.4 nothing seems to get translated into french with the supplied po/mo files or new po/mo files based on leaf.pot.
By the way. Here's the other post I mentioned above :
I tried his suggestion
>>I tried in "Poedit" option "update from a file .POT"<<
but that didn't help.