The civil registry was created in France in 1792. Thus you'll only find church records before that, whether they're protestant, jewish or catholic. If they still exist, they're definitely to be found in France (though the protestant may be written in German at times).
Most of the French records were microfilmed by the LDS so it's always a good idea to check first what they have done about a particular town: http://www.familysearch.org/Eng/Library/fhlcatalog/supermain...
For the church records of Dampierre-les-Bois, there are 3 matching microfilms:
- Parish Registers (1672-1792): Catholic church records. Parish of Fêche-l'Eglise (in the departement of Belfort)
- Parish Registers (1751-1845): Lutherian Church of Badevel (in the departement of Doubs)
- Parish Registers (1770-1782): Lutherian Church of Etupes (in the departement of Doubs)
You'll find the catholic parish registers on the Territoire de Belfort Archives website: http://www.archives.cg90.fr
Click on 'Recherche simple' and enter 'Dampierre-les-Bois'. Then click on the first result (45 E-DEPOT FECHE-L'EGLISE), then on the records miniature to access the pictures.
The other records (including the protestant records but also some catholic records and the after-1792 civil registry) are kept at the Doubs Departemental Archives Center. The digitisation there is stil on-going and right now only the 10-years indexes of civil registry (called "Tables décennales de l'État-Civil") are available on their website: http://recherche-archives.doubs.fr/
Here are some explanations on how to access/use it: http://translate.google.fr/translate?js=n&prev=_t&hl...
One of the quickest way is to choose 'Recherche guidée' and type the town name (Dampierre-les-Bois) in the 'Partout' box (partout=everywhere). Of course, for the moment, you'll find only the 'Tables Décennales' from 1793 (the 1803/1812 period is missing).
Also on their website can be found a document detailing all BMS records for each town/parish (it's a PDF file): Registres paroissiaux - Etat des fonds (inventaire): http://recherche-archives.doubs.fr/?id=recherche_guidee_inve...
If you search it for 'Dampierre-les-Bois', you'll find the various records but the time periods are the same as those indicated by the LDS. Which means you shouldn't find Protestant parish records for Dampierre before 1751.
However, if you have ancestors in Montbeliard itself, you'll be interested to learn the town will put their archives on their own website before the end of the year: http://translate.google.fr/translate?js=n&prev=_t&hl...
They will offer parish registers from 1571 (two Lutheran parishes and one Catholic parish) but also, of utmost interest, a database created by the indexation of all names found on the records (80,000 baptisms/births, marriages and burials/deaths).
Hope all of that helps you a little! ;)