UFC-Que Choisir shares news about new rules in France. These rules cover how many bags you can use and their sizes. UFC-Que Choisir is France's top consumer group. It offers independent info, advice, and fights for consumer rights. They announced this on their website.
SNCF, the French state-owned railway, limits the number of bags on TGV Inoui and Intercités trains. Passengers may have only two suitcases and one backpack. The new rules also apply to the transport of strollers, skis, and bicycles. The company says on its website: You can check up to 2 bags and one hand bag per person.
SNCF limits the amount of luggage – you can still take quite a bit with you
Violating the rules may result in a fine or denial of access to the train. You must also label luggage with name tags.
Jon Worth runs an online media outlet focused on train travel. He talks about bag rules
Here is Jon Worth's page
Jon Worth states that breaking the rules may lead to a fine. If they conduct bag checks before boarding, a passenger might be denied access to the train.
Worth also states that the labelling of bags is mandatory. Passengers must be able to move all their bags themselves at the same time, although there is no weight limit.