According to Wikipedia, citizens of France can/must have biometric passports [doesn't imply retaining biometric information].
Accroding to the US Library of Congress, biometric data collected for production of passports is also retained and may be used by law enforcement agencies in Argentina, Australia, Brazil, France, Israel, New Zealand, Ukraine, and the USA.
This may — of course — gradually create creeping de-facto databases of a large part of the population (citizens who travel).
According to wikipedia, France has a non-compulsory identity card.
In March 2012, the Conseil Constitutionnel, the highest authority on the French Constitution, declared the provisions of a law permitting judicial and police use of a centralized national ID database to be unconstitutional.