Backed by the G14 group of top European clubs, Lyon hopes to force soccer's world governing body into paying clubs to release players for national team duty.
Abidal cracked a bone in his foot playing for France last month and will be out of action until February 2006.
The clubs believe they should be compensated in such situations as they bear all the risks should players (their assets) return injured from international duty.
FIFA president Sepp Blatter, however, said it's the responsibility of clubs to insure their international players.
G14 is already supporting Belgian club Sporting Charleroi in a similar suit filed against FIFA in September.
Charleroi's Moroccan international, Abdelmajid Oulmers, injured his ankle in a friendly against Burkina Faso last year and was sidelined for eight months.
