Now, this is familiar to those of us who follow "illegal immigration" and what has been happening in the United States over the past decade.
The French have a problem because human beings are migratory creatures. When we, as a species, live in a place that sucks, we automatically and instinctually move to a place that does not suck.
Having been to France, I can tell you that it is expensive there and it is very difficult for anyone to establish themselves legitimately. There is an issue with this throughout Europe, and it can be summed up as follows: as soon as anyone hits a Eurozone country, they begin migrating to a place where they can work, make money, and establish some sort of existence. That means that they are leaving places like Africa, the Middle East, and the parts of Eastern Europe, like Belarus, that are intolerable to live in.
How do you solve this problem? Well, you could start by ensuring that the places where it sucks don't suck so bad. Once you start to fix places where people cannot live, there's a good chance that some of them will start to stay there (or even go back there). Nobody wants to leave where they are at if things turn around, and even though that is a general statement, it seems to be true because when people leave one part of Europe and go to another, they take along tokens of home. This is why you can see flags of every nation wherever you look in Europe, especially flying in the windows of cars.
France is a country in which you can live. It is a paradise to people from the aforementioned countries and regions. Closing the border will do what? Increase the number of policemen working the border crossings? Good luck with that.