There is no Utility Models in France.
If you search a shorter and cheaper protection than with patent, you should apply for a Utility Certificate. Utility Certificates confers same protection as a patent, without the expenses of search. The conditions of patentability are the same and the search report will be obligatory only when one wants to act as counterfeit.
The protection offered by Utility Certificates can last only a maximum of 6 years, if you pay annual renewals.
The Utility Certificate can nevertheless be interesting to protect inventions with short lifespan whose protection does not have to be wide abroad. To be used without surprise, it requires however a good knowledge of the state of the art.
For information about application, see the patent pages.