I'm always skeptical about beggars. I don't want to be, but the majority are either (as you said) addicts of some kind, or have made begging their profession. If the family you saw looked like Roma and were from France, then they probably were indeed Roma. And Roma are known for begging professionally. They take their children with them precisely to tug on the heart strings of tender hearted people like yourself.
But possibly - Roma or not - they really were a family in need, who were just having a bad day. I once encountered a beggar who only spoke three words in English: "for the children". He himself was an old man - I later learned that he was in his 90s. Of course he said the correct words, so although I had my doubts I gave him a ten euro note on the chance he was legit. Turns out he was famous locally for his activities - a folk saint, in fact, who lived to the age of 103 - and he gave all the money he collected to churches and orphanages. I wish it was easier to know who's real and who isn't.