I don’t recognise the design, but the company was “Trelon Weldon & Weil” (not “Wells”) and you can narrow down that presumed 1814-1865 dating to a 20=year window. The company was formed in 1835 as “Trelon and Langlois-Sauer”, Weldon joined them in 1841, but the partnership didn’t become Trelon, Weldon & Weil until 1845. They continued under that name until 1865 when they became “Trelon-Weldon-Weil, Hartog and Marchand” (TWW HM).
It looks more like part of a cuff-link than a button, although commonly these were called “cuff-buttons” at the time. It seems reasonable to guess that the red, white and blue is for the French tricolor and it might be a military insignia borrowed onto a set of cuff-links rather than being a military issue item. The emblems in the red and blue sectors look awfully like spurs to me.
I couldn’t find any match for cavalry-related badges. I mused that it might be a French Foreign Legion insignia… there are dozens of them, but I couldn’t find a match there either.