Yes, that is a real Chassepot bayonet, made at the "Manufacture Imperiale de Chatellerault" in 1869. They fetch high prices here, very high with a scabbard. You have an excellent combination of rifle plus bayonet, and if you swing it round it should be very good at trimming those flowers!
But I am flummoxed by the split ring, unless they really were adjusted for a precision fit on the rail. (Nope, doesn't sound plausible to me either!)
BTW, the rifle is marked as I predicted, and the T.1872 and T.83 stand for "Transformé" i.e. modifications of 1872 and 1883 respectively. So your rifle, Chassepot Model of 1866 was upgraded no less than 4 times - in 1872, 1874, 1880, and 1883. Just about the complete set of changes, I think.
Patrick