No, keep the gun in France!
5 Infantry, 2 Artillery, 4 Mechanized Infantry, 5 Armor
vs
1 AA Gun, 6 Infantry, 2 Artillery, 2 Armor, 1 Fighter
Because you cannot run a calculator with the gun being a casuality, I will run the calculator without the gun and with the gun as an extra defending infantry. The actual statistic should be somewhere between them:
Odds: 96.8% with 1 Mechanized Infantry, 2 Artillery and 5 Armor remaining
Odds: 91.5% with 1 Artillery, 5 Armor remaining.
If we take out the gun, then we increase the odds of success in France by 5%, but we don’t NEED to increase the success of France by 5%, it’s already over 90%!!!
If you choose to bring a fighter to the battle, one, I think you’re unskilled, two, it is your choice. I am not saying it’s bad, I am just saying I will look down on you as a lesser player and may even snoot at you once or twice. :P (this is a jest, of course, I don’t really think this way, I just wanted to be funny.)