I realize this thread is ancient, but I'll add what little I know about these ancestors I thnk we share, in case anyone else should come across this post:
Ancestry.com has a database of "Optants," who were citizens of Alsace-Lorraine who publicly declared their desire to remain French after Germany took over much of the region in 1871. Ancestry.com has this to say about these records:
"Alsace-Lorraine was a territory ceded by France to Germany in the Treaty of Frankfurt (May 10, 1871), as a consequence of the Franco-Prussian War. It included most of the region of Alsace and about a quarter of the region of Lorraine. In 1872, those who elected to retain their French citizenship rather than become German, submitted statements in the town hall and published the fact in the weekly 'Bulletins des lois de la République française'."
A search of "Regnaults" returns about a dozen results, including Louis Regnault, born Sept. 20, 1860, which matches the birthdate on his Springfield, MA naturalization card (and his various census appearances on Tyler St. in Springfield). That "Optant" record also gives his birthplace as Wittersdorff, and his home as Montreaux Chateau, Haut-Rhin. The declaration was made on Sept. 1st, 1872. The declaration was made with his unnamed father (he was 12 at the time).
There were three other "Regnaults" in these records who were born in the same place, lived in the same place, and signed on the same date: Auguste (6), Marie-Anne Regnault nee Zimmerman (50), and Francois Charles Joseph Regnault (53).
There's no guarantee that these three were related to Louis or to each other, or that these records are comprehensive and list all Regnaults who lived there, or who signed, but it might provide a lead for additional review...
P.S. Regarding your comment about Belfort, there's an obit in the Springfield Union from November 1960 that says she was born in "Belfast, France," which I would guess was a corruption of "Belfort."