If your company is already registered elsewhere in the EU and requires to register for VAT in France, including obtaining an EU Intracommunity number, the process is reasonably straightforward compared to other EU countries such as Spain.
French VAT registration is effected via the department of the Tax Office that deals with foreign companies, la Service des Impòts des Entreprises Etrangêres. Applications are made by post and processing times are generally quite quick, as little as two weeks.
Once the French VAT application has been accepted, a French tax code (SIRET) and Intracommunity VAT number is issued, with a notice sent out which explains how to file VAT returns. The frequency of presentation depends on the expected volume of operations in France of your company.