Is it normal for a hotel not to hold a room with a credit card?

No, it should not concern you any accommodation still has a recognition of the value of honesty between both parties.

Isn't it a nice change!
We have reserved in three different areas of Germany for this summer, in small hotels. No one has wanted a credit card. Mutual respect.

FWIW, I think there must be some kind of law in Germany, that forces some hotels to accept reservations without a CC guarantee. I was reserving hotels in Germany for a trip later this month, and Ibis always gave me the option of not providing a credit card number. I stay in Ibis frequently in other parts of Europe, and they have never given me this option in any other country. Me thinks Ibis wouldn't be doing this unless they had to.

The smaller, non-chain-owned hotels in Germany usually don't ask for any kind of guarantee either. In some parts of the world people still trust each other. A few years ago we went to a small local produce store in the Rhön mountains in Germany. We wanted to buy some of their self-made saussages, honey etc. but were out of cash. They, on the other hand didn't take any kind of cards, neither debit nor credit. So they offered us to take the food anyway and transfer the money (around €10 or so) to their bank account once we're back home...

Why? Some people are just trusting, strange as it seems. It's not uncommon.

Thank you for all of your help! The hotels are in Paris and Bordeaux. They seem on the level and like this is something they do often. Merci!

Our experience is that if they take a credit card the room is yours regardless of checking in time. If they do not, then you need to be checked in by a certain time or it is gone to the first walk up. So be sure you know and understand their cut off time for checking in.

And if we want it to stay this way we all have to be responsible and cancel the reservation if your plans change.

Only once did I have a bad experience in this regard. I reserved a room in Rouen France with a credit card. This was the trip where my husband was hospitalized. When it became obvious that we would not be able to get to Rouen (about 2 days before we were due there), I asked the hotel to contact them and cancel our reservation. But the hotel had already cancelled our reservation because I had not called them to confirm I would be there (with the charge card I didn't know I needed to), and they had charged our card. The charge card company was able to get this reversed. I don't know how often this happens...only time for us.

It is really important in Europe to carefully understand the rules and requirements for booking accomodations because all places are different. Some places offer steep discounts for purchasing the room in advance, but do not allow for cancellations for ANY reason. Some places will hold the room for you with a credit card, but still require you to confirm the reservation by a certain date. Some places have limited check in times and will rent to someone else if you have not made prior arrangements for a different time. Or you'll show up and no one is there to open the door and check you in. And some are very casual, just let them know you want the room and show up whenever that day and they'll have your room.