I have a little bit of French ancestry, so I have done a bit of digging in French genealogical resources. And I want to make it clear right now: I do not understand French, but have been generally able to navigate these websites, with the help of Google Translator. So if I can do it, anyone can!
Firstly, here are some French words that may be helpful as you research French family history:
The websites you might find useful will depend on where your French ancestors lived. Mine were from Haut Rhin (Upper Rhine), Alsace, and also from Paris, so that's what I'll be focusing on here.
The most useful online genealogical resource for Paris that I have found is the Archives Numérisées de Paris - the Paris Archives. The Paris archives have three sections of material - the État civil de Paris, civil vital records for Paris, (mostly 1860-1902), Sources Généalogiques Complémentaires, additional complementary resources, such as military records (1875-1921) and children assisted by the Seine (1742-1913), and Documents Iconographiques, maps (nineteenth century) and photographs related to urban planning (1860-1940). Of these records I have made the most use of the État civil de Paris. These records have tables of decades for each category of vital record - births/marriages/deaths, and then also the individual records themselves, which are listed in chronological order. The biggest problem is that you need to know which district to look in, though if you are patient, you could try all 20 districts! Use the decade tables to find the exact date of the event, and then look for the actual record itself. Below is a excerpt from the 1873-1882 marriage table for the 17th arrondissement (district) of Paris:
Taking the record for Salomé Weiss (no known relation to my Weiss family), from 4 November 1873, this is what it looks like:
This is where, if you don't understand French, it becomes slow and painstaking/painful as you transcribe it and run it through Google Translator! The record gives details of the groom, his occupation, his age, where he's from, his parents, the bride, her age, where she's from, her parents, etc. and then also lists a number of witnesses (if you're lucky some of them are identified as relatives) and then their signatures, along with the mayor - it's a civil record after all. These records can contain a wealth of useful information! Here's some of it in a bit more detail:
Haut Rhin (Upper Rhine)
The most useful online genealogical resource for Haut Rhin is Archives Départementales du Haut-Rhin - the Departmental Archives of the Upper Rhine. If you go to the Services section, there are four different types of record you can search: the Ancient and Modern Archives (Archives anciennes et modernes), the Contemporary Archives (Archives contemporaines), Postcards (Cartes postales), and Vital records (Actes d'état civil). Although there is a chance you might find something of interest in the first three sections, you'll most likely get the most useful information from the vital records. You can choose the place to search, and then search the decade tables or births, marriages, deaths, publication of marriages, or a register of the names of Jews. The information is quite similar to what you get in the Paris archives.
There are quite likely plenty of regional archives across France which hold similar records available to access online, but this is just a taster of the ones I have used.