Once they caught you, they ask for the printed document [1] either properly filled with required information or handwritten on a paper. Next they keep it, so you have to provide another one the next time.
If you don't comply with the rules, you get fined from 38€ to 135€.
If you go out to buy food or other vital important goods (soap, toothpaste, ...), you are required to go only on governement approuved shops. For now, few people succeed to get that list of official shops and you see almost everyone going were they can find food.
Honestly, people are really scared and very angry because three to four days ago, the government said everyting is fine, no need to worry, let's keep calm, let's be goods citizen, don't hurry on shops, and bla and bla and bla.
In the end, civilized people like me just understood they have been abused because while they tried to stay good citizens, bastard emptied shops and as of now, you are very lucky if you can find something to eat or even a soap, at the price of hours long waiting queue on the parking of the shops.
By the way, even before the quarantine, you couldn't buy as many goods a you wanted : since yesterday morning and in almost every shops, supply is very, very limited and you can only buy a limited number of the same item, although the limits are not official and/or legal (for now).
It's not North Korea, but it's almost like ...
[1] https://www.interieur.gouv.fr/content/download/121663/976885...