Actually, in the vast majority of the world, you're on your own when you turn 18. However, in most countries, you would have to legally evict your children, which could take a couple months. But as far as food, money, transportation, definitely not required or mandated.
In France, I could definitely see parents lying to police saying you threatened them, or were trying to kill yourself to get an unwanted child out of their house.
America is actually a bit of an outlier with this. In most countries, unmarried children (both men and women) will often live with their parents--multigenerational households are more the norm. The rates in the US have increased a lot over the past 20 years, but compared to many parts of Europe (but not, say the UK, Germany, or Scandinavia), Asia, Africa, Latin America it's still lower. Independence costs a lot of money and resources, and the economic/housing situation in most developing countries is horrendous. Even somewhere like Japan, for that matter. Part of the fact that the US has the worst homeless rates in the developed world is that a lot of parents have the old-school, 50s mentality, though it seems to be decreasing, judging by the number of NEETs posting here.
You're right though--I'm not aware of there being any legal mandate anywhere to support your children past adulthood (whether it's 16, 18, or 19). Some adult children can and have sued their parents over issues relating to this, but I'm not sure if that's evidence of a requirement. Perhaps Xion can fill us in with regard to France.
I've thought before that in a responsible society they would prep individuals for something like homelessness or destitution, but that's a level of compassion and foresight I wouldn't expect global society capable of handling. Most people aren't even raised to cook a meal, much less deal with the streets.
I'm sorry you had to experience that. People suck.
