Local Boy: It appears you have a correct model 1899 carbine. Serial number 349616 would have been built around September or October, 1901.

Your stock and hand-guard appear to be Italian walnut. This wood is found on some Krag rifles and carbines built during 1899 to 1901. The 'finger grooves' of your forearm suggest the stock has been sanded down a bit. When first built, your carbine likely had the same type of hand-guard as used on the model 1898 rifle. These were later updated to the 'humped' type to protect the rear sight when the carbine was used in a saddle scabbard.

Is there a dated 'cartouche' on your stock?

I only see a couple of minor (and correctable) problems on your 1899 carbine: Your extractor had the 'bolt hold-open pin' filed off. Your front-sight blade is a replacement and too tall. Your carbine will probably shoot low.

Nice pick up! Enjoy!