Most of them were cap and ball, made by Colt, Remington, LeMat, Spiller & Burr, Adams...

I have bumped into statements that there were at least a few pin fire French Lefauceaux revolvers used. Maybe somebody has some iron-clad documentation and will pop up here, but I don't. In favor of this, they were being made in the 1850's and had wide distribution in Europe. A French website devoted to the company here states that a Colonel Schuyler ordered several thousand- and of of course cartridges for them-in 1861, though it also says this is not certain. It's notable that there is no Union Colonel named Schuyler ( there was a Schuyler Hamilton) but there was a very large firearms company in 1861 named Schuyler, Hartley and Graham- and they could well have imported them for resale. The rate of fire with a Lefaucheux was faster than with a cap & ball, of course, as they could be easily reloaded; and greater rate of fire would be very attractive to a company selling guns to soldiers, as it would be to their customers.

Against this, any soldier/cavalryman getting one would get a problem: a Colt or Remington cap & ball revolver would come with bullet mold and take standard percussion caps, and so could be reloaded with available materials. A Lefaucheaux would need to have special imported ammunition supplied for it, in wartime, likely during a campaign. That would make any soldier hesitate to buy one.