It's difficult to tell based on the information you present but my guess is that you will not be able to use your French citizenship, if you have it. The reasons for that are a bit complex but I will try to explain the rules as well as I can.
Serving in the French army is not directly relevant as such. There are provisions to become French par le sang versé (literally “through spilled blood”) if you are injured or died in service but those are much more recent than World War II. On the other hand, soldiers (including those in the Foreign legion) could always apply for a regular naturalization and it's possible that it's what your grandfather did.
Whatever the case may be, the fact that your paternal uncle apparently is a French citizen by birth does suggest that your paternal grandfather was himself a French citizen (but you ought to check that with your uncle, if he naturalized then that's something else). If your grandfather became a French citizen before your father's birth then your father is also a French citizen. He might have some trouble proving it but there is no registration needed to remain a French citizen.
So far so good but the problem is that there are rules that make it impossible for your father to transmit his French citizenship to his children if he lived for more than 50 years abroad without possession d'état [de français].
“Possession d'état” means acting as a French citizen, like holding a passport or voting in French elections, irrespective of whether you are a French citizen or not. You can have possession d'état without citizenship if the French government treats you like a citizen by mistake. Conversely, you can be a citizen without possession d'état if you don't make use of your citizenship.
So if your father never used his citizenship (e.g. by getting a French passport) then his children are not considered French citizens. But if your father is still alive, he might still be able to apply for a passport or otherwise get possession d'état and my understanding is that you could then use your French citizenship too.
In cases like that, where the link with France is tenuous and difficult to prove, it can be difficult to avail yourself of your citizenship, even if you really do have it. So you have to expect a long procedure and ideally hire a lawyer familiar with such matters to help you get a certificat de nationalité.
Finally, it might sound like nitpicking but legally you cannot be “eligible to get French citizenship” through your grandfather; you either already have it and need to prove it or you don't and then the only options are all the usual routes to citizenship (naturalization, etc.)