I wouldn't suggest you to drink tap water as a precaution.
A recent study has shown that it has a concentration of pesticide over 8 times the allowed regulated amount for a few years.
Though there is no immediate consequence, this particular kind of pesticide is proved to be cancerous.
So if I were you, I wouldn't drink Paris tap water (I myself live near Paris), but there are no immediate consequences, it's just a risk, it's up to you if you're willing to take the risk
Edit: Ok since some people want sources here you go, I didn't want to include any because it's in french OBVIOUSLY, so good luck :
Don't just start downvoting when you don't know and you're probably not even french, it is widely known and even been on the news a few weeks ago.
-> Ce rapport révèle en effet l’existence de métabolites de Chlorothalonil dans l'eau courante de nos robinets. Il s’agit de résidus d'un pesticide pourtant interdit depuis 2019.
TLDR; This report reveals the existance of particles of "Chlorothalonil" in our tap water. They are residues of a pesticide forbidden since 2019.