From the things I know about France I can see many obvious reasons why crime might be higher. It is a very strict society compared to e.g. Scandinavia which allows e.g. children and youngster a much freer life. The French are more likely to engage in almost psychological terror against their children. Well behaved children who don't make noise and sit still is valued in France, while Scandinavians are far more tolerant towards the natural behaviour of children and perform very mild sanctions towards bad behaviour.
France is also a more elitist and technocratic society, while Scandinavia is more egalitarian and cares more about the common man than the elite. The dehumanising vast monotone areas built in France which are now rife with crime would never have been built in a Scandinavian society.
I know I sounded very negative now. I didn't include all the wonderful things about France, because the whole point was to highlight why it isn't just a matter of having different people. The organisation of society creates the people.
The same could be said about the US. It is a society organised to produce violence.
Second, France isn't a war zone and most of us live pretty safely and happy over here.
More importantly, do you know for sure that the situation would be better with harsher prison sentences?
More seriously, the problem is not so much homicides than common criminality. Courts almost always give suspended sentences for petty crime, and even when the judge does not suspend the sentence, the policy is to automatically suspend it behind the scene afterwards if it's less than 6 months (juge d'application des peines). And if a criminal still ends up in jail, he would only ever do between half and two third of the sentence. The whole system is designed to be toothless.
The example of New York City under Giuliani is a pretty spectacular example of the impact of a tougher penal policy against crime. I am not suggesting this should be the only response but I do think that no response will be efficient without it.
According to what I could dig up from Google, it's had a homicide rate of 1.2 per 100,000 people and a serious assault rate of 299 per 100,000 people over the last couple of years.
Those are respectively slightly higher (1.2 vs 1.0) and significantly lower (400 vs 299, although data collection methodologies may be different) than the UK where I live, which is generally considered to be a reasonably safe country crime-wise.
(Didn't really have time to dig into other crime categories - would be interested to hear if they buck the trend.)
Not claiming your statement isn't true, but unless I'm misreading the statistics the effect doesn't seem to be a massive crime wave.
[1] https://www.aclu.org/report/living-death-life-without-parole...
The police doesn't even bother charging criminals as they systematically walk free. Criminals accumulate dozens of offenses on their criminal records in complete impunity.
Denmark, Switzerland, Norway or Sweden can afford to have very lax justice systems because they have a population that commits little crime. But with a different population these systems would just fall apart.