Even France, the famous country of asylum and human rights, people that flee their countries are not welcome, by both native and administration.
It would be infinitely preferable to die trying what you can fix in your lifetime, on your native soil, than fleeing somewhere and bet for that 1% scenario where you will have a decent new life.
As someone who is seriously considering to migrate somewhere else (has nothing to do with asylum seeking tho), must tell you that I haven't considered France at all. Choice will be made depending on the job I manage to get in a foreign country. Countries where I could move, live and work are Scandinavian countries because of their lax legal immigration laws, Canada, USA, Australia. Even Russia.
Most EU countries are hostile to any kind of immigrants, because they had to accept many people coming from former colonies as their citizens. UK has to be the worst by far on that list, followed closely by France, Netherlands, Denmark. It's excruciatingly hard to move there to live and work, even legally, if you come from non EU countries.
Also, chance that someone coming from country at war will live better in some other country is not 1%. It is certain or 100%. Do some research about life in today Ukraine and you'll realize that it has to be one of the hardest countries to live in a decent manner. Now imagine what will happen if war starts and how worse can become. It can always be worse, that is something I learned living in my country. There is no bottom.