Second master and phd in math after phd in mechanical engineering
My story is somewhat similar to yours. I did statistics, then switched to math as I found I love it. Here is my pathway in France. I didn't restudy the whole bachelor. I applied for (and got accepted to) the 3rd year undergraduate at a French uni. After that, I applied for (and got accepted easily to) the 1st year of master (aka M1) in math at a top French uni (as I got good marks). If my mark is good enough, I can apply for the 2nd year of master (aka M2) (in France, 1st year and 2nd year of master are seperated, you have to apply for both seperately).

So, for your questions:


I would highly recommend you to retake the 3rd year undergraduate (aka Licence 3) in math, and it should be sufficient for you to go further. As you have a technical background (and even better, at PhD level), it's not difficult for you to get admitted directly. The chance would be lower if you apply directly for the master in math because the math in France is highly theoritical, they would prefer someone with a math degree for the master degree in math. Of course, if you can show that you have done sufficient advanced math (especially topology, integration, measure theory, which are a must if you want to do PDE), then no problem. However, due to French-style math, I still recommend you to start from the 3rd year of bachelor rather than 1st year of master.


2) If your mark is good, you can apply for many masters at top uni (like Paris 6, Paris 11, which are strong in applied math, including PDE) or "Grandes Ecoles". Also your chance to be admitted to a PhD in math should be good as well. Applied math is, at least easier to be admitted than pure math.

3) Even though you have two degrees, they are quite closely related. So I don't see any problems with that. Actually I think you even have some advantages to others.