Customs officer will open your passport to the ID page since no custom officer is that mentally impaired (although there are some fine specimen out there) so as to believe what the cover says. And what is the difference between having French passport cover and one of those shine-bright-like-a-diamond Victoria Secret passport cover? Maybe they will think you are not as good looking as a VS model and that will rise suspicion of your identity? My sister has one of those and she has never took the passport out of its cover for the sake of a customs officer.

Of course if there is strict announcement to have the passport taken out of its cover, then do so. Otherwise, I wouldn't stress out about it at all.

Safe travels!