Those are not the only two options that they can choose from. And being hit is a very minimal example. Would you say the same for rape? No punishment required; just apologise and work on yourself?
You skipped the “take responsibility”. In case of a more serious crime a simple apology is indeed not enough. But it should still be possible to proceed with something more productive for everyone than putting the perpetrator behind bars. As you say, there are many options.
I think most people who commit a crime either do it in the heat of the moment, or believe that they're very unlikely to get caught. The distant prospect of punishment doesn't apply in either case.
I guess there are some edge cases. Drug smugglers for example are probably aware of the rough probability of detection and weigh it up against the length of jail time. But I reckon Sarkozy thought he'd just get away with it and didn't even consider what the potential punishment would be.
> those who spend a lot of time in prison seem to come out worse and reoffend. How is that helpful?
You're implying that imprisonment makes people offend more - perhaps the simpler explanation is that most criminals will commit crimes when they get the chance, especially prolific criminals. Prison takes them off the streets and stops them victimising more people - this is helpful.
Prison is nonsense and a waste of human life. Best punishment is caning like Singapore. Do fast and quick. Pain is an excellent memory aid. Most stable lowest recidivism rate.