Someone has mentioned a possible solution to reducing the numbers. Be less welcoming. Glare silently at those arriving. Insist that they speak English, give lessons and remove interpreters. House in 'barracks' with adequate canteen meals - no giving way to food preferences or demands for halal foodstuffs (the Koran permits non-halal if halal is not available). Earn their food by working at something - I don't know what, something to ease poverty amongst the indigenous inhabitants.
Legal immigrants into France are not permitted to access the social security/health system until they have supported themselves for 5 years. Be kind, make it 3 years.
OK it's harsh - but they have no right to come here illegally. If I act illegally, I expect to be punished.