I am not sure I understand the details of the episode.
There are two daily connections ETZ-PUF, both through LYS. Maybe, only the afternoon one operated in that period, meaning that the next option was the next afternoon.
Instead, FB recredited the miles fully and offered a free ticket CDG-PUF, if I understand correcly. The OP accepted the deal. Basically the OP got a free CDG-PUF ticket and had to pay train ticket Metz-Paris.

Then the OP wonders if she can get reimbursed for the train ticket to CDG and the hotel night in CDG, plus a 350 compensation.

As NickB says, this is debatable. If A5 does not willingly wants to do more than what the OP already accepted, it seems to me a hard case to file. Yes, the OP arrived late in PUF, but the OP accepted a full refund of the original ticket plus a free CDG-PUF as commercial gesture.
If the OP had been taking the next-day flight, she would have been entitled to care (hotel night in Metz) and EC 261 compensation for the delay. But in the actual scenario, I doubt.