Mike -Since you only provided limited information and one photo, I must return the same... With some comments.
Earlier Elcee's were number-graded as a rule. Thus, a field grade gun might be expected to carry a "O" or "OO" stamp. Your gun carries a "F" and I expect the tubes say "Field Grade" and identify it as a Hunter Arms product. If so, then it's birth date is somewhere around 1919. If not, then it may be a Syracuse gun and I don't have those dates.
Rare? It depends on your definition of rare. The gun has been refinished. Improperly I might add. Checkering has been removed from the stock and I see evidence of a crack behind the lock. Further, I question the tubes. If they have a spiral pattern, then they're damascus. Finish would have been brown.
If's...
If the tubes are damascus and the gun remains in good mechanical condition, then light black powder loads might just be fun.
If the tubes are fluid steel and mechanical condition is good, then I'd have the chamber length checked and use light modern loads. (Chambers will almost certainly be too short.)
My conclusion...
Any Elcee in shooting condition is a bit of a treasure. Yours has been redone and some of the most beautiful components removed or improperly restored. This puts the piece squarely in the shooter class (depending on actual condition). As such the gun is most probably a $300.00 +/- piece.
I'm really sorry to offer my opinion as it seems that either you have built yourself up to some rather lofty conclusions, or someone else has. In either case I fear disappointment. I'm not fond of being the bearer of bad news.