An objective estimate? Not possible, unless we're talking bare gold value and nothing else. Everything in this hobby is subjective... As is said before, the dial has been refinished, so my guess would be around gold value + $50 or so.
Why do you think it is a French market case? It is not - it has a squirrel hallmark which was used for 14K in Switzerland...
On the inside of the caseback or on the dial? The logo on the inside was also used in non-French cases early on. The logo on the dial is incorrect, as the dial has been refinished.
Prior to the 1930’s, that was Omega’s logo worldwide. The French importers kept it after WWII. It’s a shame about the dial. The watch looks nice otherwise. I agree with the assessment of gold value, plus $50 to $100 for the movement. Hope this helps. gatorcpa