It's difficult to find comprehensive up-to-date information about this in English. The most useful official source is vosdroits.service-public.fr, in particular the pages Européens en France, Citoyen européen ou suisse : installer sa famille proche en France and Famille d'Européen en France : demande de carte de séjour "UE" (all in French).
For simplicity, I will write this answer as if “you” are the third-country citizen in need of a carte de séjour. Your “sponsor” is your spouse (the EU citizen with whom you are moving to France).
What you need is a carte de séjour, mention « UE - membre de famille ». To get it, you should bring the following documents:
- Valid passport
- Proof of your relationship with your sponsor, e.g. a marriage certificate
- Proof of the right of the sponsor to stay under treaty rules, e.g. his or her work contract
- 3 photos
It might be best to go to the préfecture with your spouse and to make sure to have some official ID to prove his or her EU citizenship. Each préfecture has its own rules but typically, you have to make an appointment in advance and wait in line (even though it's on appointment only…).
It might be necessary to get a translation from a sworn translator for all documents in a foreign language, but I am not entirely sure whether this also applies to documents from other EU countries.
You should receive a document called a récépissé on the spot, which should be valid for 6 months and will allow you to wait for the actual card (which might take several months to be issued). It's annoying to have to wait so long and to be without visa or permit for some time but as long as you have filed your request in time and you have your récépissé, you don't need to worry about the 3-month delay.
The answer does not change if you want to work, as the spouse of an EU citizen, you have the right to do that as a matter of course (people with other types of visa/carte de séjour might not). First apply for the carte de séjour and use it to prove you have the right to work in France.
All these rules apply to the spouses of EU/EEA and Swiss citizens (except Croatian and French citizens) who reside in France under freedom of movement rules. Other people have to satisfy other requirements like presenting their spouse's work authorization (for spouses of Croatian citizens) or a undergoing a medical check-up (for spouses of French citizens and many other applicants).
Finally, as far as terminology is concerned, a “titre de séjour” is anything that gives you the right to stay in France. This includes several types of carte de séjour but also something called a carte de résident (not relevant in your situation but that explains the slightly confusing distinction).
