Upvote:4
As you are traveling with your British wife, you can benefit from the European Union's right of free movement, at least while the UK remains in the EU. You should therefore apply for a Schengen visa as the family member of a Union citizen.
This means that the application and the visa should be free of charge, and that it should be processed quickly. It also means that certain items on the visa application form do not apply to you. These items should be indicated with an asterisk; they are the questions that ask about your occupation, sponsorship, and expenses.
For more information, see Directive 2004/38/EC on the right of free movement and the Schengen Visa Code.
France uses TLScontact to handle its visa applications in the UK. If TLS contact charges a fee for its services to free-movement applicants, then you should also be able to apply directly to the French consulate or embassy so you can bypass that service fee.
As suggested in a comment, you do not need this visa if you are an "Annex II" national, that is, if you do not normally need a visa to enter the Schengen area. In that case, you should bring a copy of your marriage certificate as proof of your relationship with your wife in case any questions arise.