Here is a (non-exhaustive) list of franchises/game studios that have explicit fan content policies that, in my option, allow fan games to be made.
NOTE: THIS IS NOT LEGAL ADVICE. I highly recommend you read these for yourself and make sure you understand exactly in which forms fan content is allowed, and ensure no changes prohibiting it have been made since I made this post.
- Joey Drew Studios https://joeydrewstudios.com/fancontent
- Armor Games Studios https://armorgamesstudios.com/fan-content-policy
- Riot Games https://www.riotgames.com/en/legal
- Innersloth https://www.innersloth.com/fan-creation-policy
- Epic Games (the studio) https://legal.epicgames.com/epicgames/fan-art-policy
- Minecraft https://www.minecraft.net/en-us/usage-guidelines
- Popcap https://www.pocappstudios.com/fan-content-policy
- Big Blue Bubble https://www.bigbluebubble.com/fan-content-policy
- Larian Studios https://larian.com/fan-content-policy
- Rovio https://www.rovio.com/rovio-fan-content-policy