I appreciate your advice.
For the moment, I am looking for a used part or for a repair kit somewhere in Europe.
I only need the broken arm, not the whole regulator, which is very expensive to replace.
But it does not seem that there are some replacement arms on the market. Only Bud's is proposing a kit to reinforce it, but it has to be welded.
There are also some used regulators for sale on Ebay, but these parts are sold in the US, and the cost of shipping to France is prohibitive.
So, I am still looking around, and will get it welded if I don't find any other solution (it has to be welded very carefully to get it to its original shape).