DEFINITELY not an Aydt..
That projection you see is the tail end of the breechblock of the martini action. With the breechblock in place, it covers the slot in the reciever that allows cleaning the bore from the breech end.
The breech block can be removed easily, and that slot allows a cleaning rod to pass.
That rifle is what a local collector gentleman callls a "Swiss-style" Schützen Martini. Lucky booger has about 5 of 'em...
As for "approximate value"... well.. the gentleman in my gun club that introduced me to these here single-shootin' rifles says that the rifles he has (of the same sort, mostly fairly simillar) go from $1500 to $2500. Depending on various things known to collectors.
It would not be unusual for you rifle to be chambered in 8.15x46R (but may also be chambered in other cartridges).
Put it on gunbroker or auctionarms, with a $1500 starting bid, and I think you'll like what it goes for.
heck, if it had a left handed stock, I'd send you $1800 for it right now
It's really a very nice rifle!
You might consider getting dies/brass for it and shooting it rather than sell or trade it off!
Paul F.