In France, N26 or Revolut issue (virtual) debit cards. The organizers called them “credit cards” because they have MasterCard branding and that they are accepted everywhere where credit cards are (including online and abroad), which isn't necessarily the case for other debit cards. Other than that, they really work like debit cards, all transactions must be authorized online and you need to have a positive balance on your account for a transaction to go through so you need to put money on it beforehand (that's what they mean with “rechargeable”). You can also use them to withdraw cash (with some restrictions) and won't incur the fees and interest you would on a pure credit card.
There is a lot of confusion around the credit / debit card terminology in France because separate credit cards are not that common. Many people just have a single card issued by their bank that works in the way I just described or maybe with payments delayed until the end of the month (“débit différé”). Conversely, there are no shops that would take debit cards but not MasterCard or Visa-branded credit cards. So everybody uses “carte bancaire” and “carte de crédit” or simply “carte” or even “carte bleue” interchangeably and you shouldn't read too much into it.
The other implication is that even though they work like a bank account with a debit card, it's not really a full bank account, hence the somewhat confusing “rechargeable credit card” (incidentally, I think N26 is actually a bank).
That said, I am not sure this solves your problem: Signing up with Revolut and N26 in France involves claiming that you are a tax resident and probably uploading a residence permit. Opening a bank account theoretically ought to be possible for non-residents but traditional banks won't be easy to deal with from abroad and leading online banks typically require a pre-existing account with another French bank, proof of address, your last tax return, etc. Transferring money from a bank account in another currency will also probably incur fees.
The only advice I can give is that you should really look into what's available in the place where you are based (India?) rather than take advice from the organizers or try to open an account in France. The most difficult thing will be getting this honorarium transferred to your account, though. I am guessing they expect an IBAN and I don't know where to get that easily if you are not a resident.