Anybody with experience in a similar situation?
I don't, answering only based on my knowledge of the rules.
Is a visa needed for the layover in CDG? If so, which visa?
Indian citizens generally require an airport transit visa in this situation but there are exceptions designed to cover people who live in the US. Unfortunately, the way US visas work makes this a little difficult in practice, official advice for the French government is that you don't need one if you hold “a residence permit guaranteeing the right of return and issued by […] the United States“.
This should obviously cover a green card (“Permanent Resident Card”) but neither “work permit” nor “residence permit” are, as far as I know, the exact name of any US documents so I can't tell if it would cover the document you hold. One thing you could do to ascertain this is to check a database called TIMATIC (see Ordinary Traveller: How to use Timatic?). If you see your document listed, you should be fine since that's probably what the check-in personnel will use to decide if you should be allowed to board your flight.
If the exception doesn't cover you, then you would need to apply for an airport transit visa (ATV). You should apply to the nearest French consulate (in practice, in the US, you apply through VFS Global). You can apply between 6 months and 15 days before travel, the sooner the better. A Schengen visa (even an ATV) costs €80 plus a $35 service fee from VFS. It might indeed be required to present yourself physically to a VFS application center, especially if this is your first application and your biometrics haven't been enrolled in the relevant Schengen database.
If yes, what happens if you travel without the visa?
You would be stopped from boarding the first leg of travel and never reach CDG. Deputizing airlines to enforce restrictions and preventing you from traveling in this situation is the entire point of the airport transit visa system, nobody is checking whether you have one after landing.