The early examples had reworked original barrels, see below.
Yours has a later purpose built barrel which dates it to 1938.

 

Thank you

 

It is RT60791. MF is the code for who provided the steel for the barrel called in French as the pourvoyeur de acier which was Manufacture Française d'Armes et Cycles de Saint Étienne or also called as ManuFrance or 'La Manu'. The circle J is for Ingénieur Militaire 2ème Classe Henri, Eugène Jeantrel who was the Directeur de Manufacture (Director of Manufacturer) of Manufacture Nationale d'Armes de Châtellerault in 1938.

 

That’s great. Thank you so much!

 

May be 45,000 R35 have been produced on the 100,000 originally planned. The overhauling/modification/assembly was made at Tulle.
The serial number given to your “shortened rifle” (officially, it was not a musketoon or carbine) comes from a Lebel made at Tulle in 1892 or 1893. But it is not very important since the original serial numbers were erased during the overhauling process, all the reused parts melted or sometimes even replaced.
10,000 have been made with MF barrels like yours. You have, like Staffy, the SACM rear sight, considered as the official R35 rear sight even if different from the one made by MAC.
Two variants of stocks exist. 80% like yours, 20% have a bar. French collectors call them « Artillery type » and « Cavalry type », a modern distinction and collectors invention. The one you have is a re-used stock. Those with a bar, a replacement stock when the R35 rework has been done. As simple as that, no “Cavalry” or “Artillery”.
1938 is the date of proof of the barrel. Probable reception the same year or in 1939.
They were supposed to be given to Artillery and Transportation Corp. During the phoney war, they are seen in the hands of Transportation Corp at first (aka Train). There is one known picture of such a carbine in the hand of a GRDI guy (reco unit).
After the fall of France, seen in the hands of Vichy Colonial Artillery and also the weapon of choice for Free France Cadets (Free French Officers School) during ceremonies.
The one shown by Staffy, with a shortened old barrel, is rare, but the rarest are those made with a MAT new barrel.
Those made with a new MAC barrel are the most common (more than 50%). Only 5,000 have been made with MAP barrels, and 4,000 with SACM barrels. About 3,000 made with old shortened barrels.
Those made with new a MAT barrel are the rarest, if we except prototypes, only one surviving carbine with such a barrel is known.
At least 50 instruction carbines, serial number without prefix letter, have been made with out of spec parts, and may be 500 for German occupying troops. Those are a little suspect since all of them are in the US where a Waffenamt add value to whatever firearm.

 

That was very comprehensive and much appreciated. I enjoy the history and background on these arms.