This is by far France's biggest problem. I had the "privilege" to tell that to our president Hollande, and he just confirmed he does not even understand what's wrong with that.
The employee can then request a reexamination in front of a court (prud'hommes). If you have any proof it will cost you 0€, you don't need a lawyer when going on prud'hommes and this will take you max 1 hour of your time. You can then ask some money to the employee to cover the damage caused and the time lost.
If you don't have any proof, then yep, you're fucked, and for a reason "presumption of innocence".
Cool for you to meet M. Hollande, but I'm afraid his role is not to vote laws or change the labor code, other instances less centralized are already dealing with this.
I don't think it's easy to demonstrate a steal. Even if you saw the guy, it will be your word against his, and court rule 8 of 10 against employer.
Not being an overachiever is by no mean a reason to be fired, not in France.
Things are changing slowly though, new types of contracts are being voted. They should bring "Flexibility". Give France a few years and you will be able to fire someone just because he's wearing a yellow shirt.
Given the mindset of french workers and unions, this new type of contract should actualy lower the overall productivity.
Entirely your fault, deal with it. The guy you hired is not responsible.
"He doesn't give 120%" Illegal. You don't force someone to work for free.
A good reason would be that he gives only 50%, not that he stole the damn coffee machine... Wrong mentality here imho.