Kids-stay-free hotels

What are the age of the children? Second, most pricing in Europe, including hotel chains, is per person.

As Frank says, most traditional European hotels price the room by the person, particularly because they include breakfast. Those that don't are probably way more expensive per room, no matter how many people, and then add on a very big added price for breakfast.

Ibis is a chain, the website says:

TRIPLE - Room with a large bed and a bunk bed
Children policy :
Accommodation is free for 2 children under 12 years sharing parents' room, a 50.00 pct discount is applied on breakfast.

Hotels in France (and no doubt other countries) are very strict about the number of people in the room. If the room is a double, only 2 are allowed. A triple - 3 people.
Some hotels have family rooms which will hold more. One chain to consider is Citadines which have aparthotels, with kitchenettes and seating areas. A good thing to consider as rooms also tend to be very small.

A typical room will have one double bed or, in the case of Germany, two beds pushed together. Definitely not 2 queens or Kings.

If you look on Booking.com or trip advisor, you can look for room and bed size. We booked with the hotels directly and always got the same price.

Have a look at Kinderhotels:

http://www.kinderhotels.co.uk/family-holidays-hotel.html

I don't know if kids are free, but these hotels have lovely facilities for families.

Overall, I think you will find wide variance, even within a chain, as local laws can be different. Best to just look at the fine print when searching on sites like booking.com as rules for families will be clearly indicated.

Look at apartments.