My Boyte family is also said to have a French connection, with a couple differences. One, I show the name spelled BOIT, originally, and 2, my line came to MS va NC and VA.
I show the name spelled a variety of ways, of course. The 1821 Marion co, MS marriage record for Shadrack is BOYET, then the 1830 Lawrence Co census is BOYT, and so on.
What I was told, the first Boit to come over was Bruce, born in France, ca 1760. He sailed to America in 1780 and in 1797, his son, Carey came to America, looking for his father, whom he found in Charlotte, NC. I have a wife for Carey, PATSY (??) Barker, and children: George, Buryl, Thomas, Shadrack and Bob. Daughter Stella died in SC. I have info that Carey came to MS in a covered wagon, ca 1815, but have been unable to find any trace of him. Shadrack is the first one to show up, in 1821, when he married Sarah Wallace, a widow with two sons.
I doubt any of this will be familiar, but yours is the first post I've seen with a French connection, so I thought I would take the chance. I''m sure the evidence is there, but has been overlooked because there is a Thomas Boyt in Va ca 1704 and assumptions were made.
If you think there is the slightest chance of a connection, please contact me. Digmup41@aol.com