Looks like an early Liscica powered Reverso. Probably circa 1932/33.

No normal parts house will have these. Let me see what I have, I may have some cal 412 parts.

Do you have a photo of the existing center wheel?

You will have to shrink the size of your photos with an image editor or post a link to them.

It looks like a fake, unfortunately. The movement finish looks Chinese.

It corresponds to a 1965 movement manufacture date so it is plausible.

It's probably a French market watch, circa 1933-1934.

What does the dial look like?

The dial is legit, the current service cost for a Futurematic is $600.

It's a U.S.A. market watch, for which JLC Switzerland has no records. Sometimes, if there is a number. in addition to the case a serial number of the case back, that is the case reference. I can service your watch at approximately 1/3 of the factory cost, assuming no parts are required. See here: ht...

The 2 register ones usually have UG movements in them.