This is reductive to the point of misleading. France does control its borders, but has chosen to accept the freedom of movement of Schengen, become a party to the Dublin Regulation, and participate in Frontex.
The idea that France is helpless to deal with the question of how it treats the migrants and the asylum seekers within its borders because of these agreements is to absolve them of responsibility towards people that they have taken on through those choices in addition to their own domestic law.
Telling people they can't work at all in your country, when they have nowhere else to go, is cruel. That is a choice France -- and other countries like Germany -- have made, and should be held responsible for.
(PS, I also disagree with the characterisation of the European borders as 'porous', given how much money, manpower, and how many human lives are expended enforcing them. If they were porous, people would not be drowning in the Mediterranean trying to reach Europe.)
Nowhere do I, or would I, try to absolve France or any other country of its responsibilities. If you're in France with no legal basis, you can work. You can sign a regular work contract. Moreover, a work contract or the promise of one, will (at least in theory I've never tried it) let you get papers to stay. The instructions are [here](https://www.legalplace.fr/guides/promesse-embauche-sans-papi...). If you apply for asylum, you cannot work for 6 months, but you will receive an allowance during this time. Instructions [here](https://www.service-public.fr/particuliers/vosdroits/F2741). France has at various times taken in "lots" of refugies. Most recently returning colonists from Algeria, but also Spanish, Portugese, Russian and Armenian, as well as "poor" immigrants from a string of places. France, unlike some of it's neighbours, operates a "droit du sol" citizenship policy. Immigrants and/or their children can become French.
Which is not the case of most migrants, including those that arrived illegally / whose stay is illegal: they are economic migrants who just want access better conditions of living (or take advantage of Jus soli/free education/free healthcare). Regardless of why they are here, they aren't refugee whose return to their country of origin is blocked by civil war.