Have you tried http://en.geneanet.org/
Or the phone book: http://www.pagesjaunes.fr/pagesblanches
Anjoutey is a very small village (less than 700 inhabitants) so there are good chances that the Isidore & Roger CHAPPUIS still living there are somehow related to your family.
I've also found a newspapers article about Isidore CHAPPUIS from 'L'Est Républicain' of May 22, 2012: https://docs.google.com/viewer?a=v&q=cache:aJVbaDkwMgYJ:...
It says Isidore & Renée CHAPPUIS, from Anjoutey, are celebrating their diamond wedding anniversary (60 years of marriage) in company of their family (3 daughters, 3 grandsons). Isidore was born in Anjoutey on January 8, 1929 and married there with Renée ARTEL in 1952. They left Anjoutey for Belfort where Isidore worked as mechanic/driver for 40 years but came back when they retired. Isidore was member of the town hall council for 2 terms of office and they are both active in the village life, particularly in the 'Amitié' (Friendship) association.
Isidore's ancestry isn't mentioned but I've found one François Isidore CHAPPUIS that very well might be his father (he married in 1927): http://gw5.geneanet.org/raymonde7?lang=en;pz=frederic;nz=bas...
Your ancestor Nicolas CHAPPUIS (1760-1847) married Jeanne Claude FOUEY (~1767-1822) in 1788 but he also married again in 1845 with Marie Catherine MERLET (1781-1857), who had a child born out of wedlock, Thomas François (1825-1896), that he legitimated and to whom he gave his name: http://gw5.geneanet.org/raymonde7?lang=en;pz=frederic;nz=bas...
François Isidore (junior) CHAPPUIS is the grandson of Thomas François: http://gw5.geneanet.org/raymonde7?lang=en&pz=frederic&am...
You should try contacting these people, I'm sure they would be pleased to know more about your branch of the family.
By the way, if you don't already know of it, take a look at LISA90 website: http://www.lisa90.org/
This association indexes a lot of Territoire-de-Belfort archives, including Anjoutey from 1775 to 1900 (choose Anjoutey in the list on the left, EC ancien = parish registers before 1792 / EC moderne = civil registers after 1792). You'll find many of your family members there but no Etienne CHAPPUIS was born in 1808? In fact, the only Etienne from Anjoutey is born in 1841, son of François-Xavier (himself son of Nicolas CHAPPUIS & Jeanne Claude FOUEY ) and Marie Catherine TISSERAND.
They also have passports for people who emigrated to the USA (choose "Pssports. Ht-Rh." in the list). There's one François-Xavier CHAPPUIS, metals worker from Croix, living in St Dizier, aged 27, who left France in 1854 going to New-Orleans in order to establish there. Also the likrly same above mentioned Nicolas François CHAPPUIS, aged 64, farmer from Anjoutey , living in Guebwiller (Alsace, dept #68) left on May 4, 1857 with his wife Marie Catherine TISSERAND (aged 52) and son Jules CHAPPUIS (aged 17, ribbons weaver), going to New-York... Could it be Jules = Etienne and first names were mixed?