My limited experience is from researching a Napoleonic era soldier who came from the Doubs. Paris would have been ‘Seine’ before Napoleon’s reorganisation.
Familysearch has many French records online, but at times it requires a search in a register/book that must first be downloaded.
The main entry point for searching in Paris is http://archives.paris.fr/ and for the neighbouring departément of Yvelines (contains wealthy suburbs of Versailles + St. Germain-en-laye) it is http://archives.yvelines.fr
The “Tables Décennales” in the above are compilations of birth, marriage, and death records from village / commune (by arrondissement in Paris) civil registrations, organized alphabetically by surname and these approximate to Ireland’s GRO records but are maintained at a local level. There is no ‘central’ repository, you have to search locally. That is the main ‘hump’ to overcome.
There are several volumes of the Bulletin des lois de la République Française available on Googlebooks. These contain much useful information – they are similar to the UK’s ‘London Gazette’ and they cover huge ground, even at times including the names of those in receipt of military pensions.
Ancestry.com also has many French marriages online, I recall finding the son of my topic in Marseilles where he was married in the early 1800’s.
Best of luck with the research