An Estonian company can be sued under French law for violating French law in France, and so can its officers, no matter what their nationality or where they reside. So yes, you could be sued in France as an officer of the company.
If you have assets in France, a French judgment against you will be easier to enforce than one against someone who has no assets in France. This is, similarly, not about nationality but about the location of your assets.
A suit could also be pursued in Estonia. If the activities in Estonia are contrary to Estonian law then you could also be sued in Estonia as an officer of the company.
We frequently have questions about "which law applies" for cases that span multiple jurisdictions. The general answer is that all law applies. An activity in multiple jurisdictions must comply with the law in every one of them.
If you are doing something that is prohibited (or even that possibly might be prohibited) in either Estonian law or French law, you should take professional legal advice. Unless you can find a lawyer who is qualified in both countries, you will need two lawyers.