The watch in your pictures is a French case Omega Constellation from the 50's. These cases did not have a reference number. Most likely the case is signed PGF which was the maker of the case. These cases tend to have a more rounded lugs/caseback compared to the regular Swiss Omega cases from this period. On the outside of the caseback you can see the French Eagle's head hallmark. Some of these French Constellations were signed "Fab Suisse" on the dial, but not all of them. There are some threads on this topic if you want to find more info.
To me everything looks fine. I am not 100% sure, but I think the crown could be original also. I believe it will have a caliber 354 bumper automatic. Note that the dial appears to have some spots on it (mostly visible in your 1st picture). The bezel seems more rounded than it should be so most likely it was polished at some point.
These are nice watches, but normally they are not as desirable as the regular Swiss Constellations.
Whether I would bid on it would all depend on the price. I purchased one of these several years back in a similar condition and paid around $1500.
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