I'm not even going to talk about the fact that I disagree with you on the opening or closing of borders. I'm just going to explain you that Europe gots 1700km of borders.
You want to keep them? Fine. So first you need some kind of wall or fence. Let's say it costs nothing to build and maintain (it'll cost a hella lot of money but let's just forget it).
You need something like a guard for every 100m on average, otherwise it's useless. makes 17 000 soldiers
You need in fact 3 soldiers for each 100m because they work only 8h a day so it's more 51 000 soldiers
For every 3 soldiers you also need on average at least one person in the backline in charge of something, that might go from cleaning the camp to radio coordination. So 51 000 soldiers plus 15 000 suport persons.
Each of them has to be paid 1 500 a month at least when they're in activity. That's 100M a month. 1billion every year. Only in salaries, I'm not talking about any kind of equipment, wall construction or anything.
Seems like a good idea to you?