The logic of the system is simple: In the EU, only the state where you reside is competent for driving licenseslicense issues. As a rule, other member states — including the one where you originally obtained your license — should refuse to issue a (duplicate) license. It's sometimes possible to fall through the cracks depending on the kind of evidence required to establish that you are a resident but, as long as you reside in France, you should not be able to ask any other EU member state.
Planning to leave soon adds a twist to your story but doesn't fundamentally change things. You first need to actually move and obtain all the necessary paperwork to prove you are a resident there before being allowed to apply for a license. Since you wouldn't have a currently valid license to hand in, it might be possible to apply for a new one based on a document issued by the member states where you originally obtained your license (that's how it works when a license is stolen). You wouldn't necessarily need to wait for 4 months and I don't think you would be doing anything illegal provided you are really a resident in the country where you apply (whether it's Poland or any other in the EU). On the other hand, merely planning to move is not enough and you wouldn't be allowed to drive out of France without a license.
As long as you live in France, you have to follow the French rules and therefore to apply forapply for a French driving license, undergo a French driving licensemedical exam, etc. It's mandatory after committing a driving offense to make it easier to track penalty points (article R222-2 of the French Code de la route). That's true even for less serious violations that do not result in any suspension. In your case, the exact rules depend on the details of the offense but it's likely that the penalty points would last 10 years (meaning that another violation during these 10 years could result in a permanent ban on driving in France).