Hi, Judith I dont know if there is a connection, but the name Beaujeaux is pronounced Bo-Jay, with the last part sounding like the French "Je" if you are familiar with that.
My mother was a Beaujeaux ...her ancestor, gggrandfather Francois, supposedly came to America in about 1834 from Alsace-Lorraine, France.He and at least one brother entered the US thru Galveston, Tx.I believe they were Huguenots, Protestants who were being persecuted by the Catholics in France. Anyway, Francois settled in St. Tammany Parish, Louisiana where he was a cattle ranchers and butcher.
Whether or not any of his siblings made their way to Arkansas is unknown.So, it maybe stretching a bit to make a connection here, but who knows?I have been doing genealogy for about 20 years and am always amazed at how names can changed over the centuries.
I will be happy to share anything I have to help you.