Illustrations of the above:
France didn't send its (only) carrier. OK, it's under (light) maintenance, but this is not rushed to make the ship available either (as it was for Libya).
France did send a BPC (Dixmude) (a very able helicopter platform), but... without helicopter onboard, just as a heavy capacity carrier (armored vehicules, numerous trucks and so on).
I too suppose there is a reason to do so.