Most countries that you phone to from abroad require non-dialling of the initial (0) in the area code of any individual phone number, including France, but this is not universally true, and you should consult your telephone directory for dialling procedures for each individual country.
Not dialling the first (0) is an atavism from the old mechanical dialling systems that has persisted into the digital age, though some countries have actually done away with it.
The first (0) in the (00) code for an international call as well as in any local area code such as (011) was actually used to tell the mechanical phone system that this was not a local call -- it's the second (0) in (00) that told it that the call was international -- whereas the (11) in (011) told it that a specific area within the national grid was being requested.
The initial (0) in (011) for an international call was left out because you had, in fact, already dialed it by having dialed (00) -- even though you need the individual country code between (00) and (11).