In the documentation (https://docs.gitea.io/en-us/https-setup/), it is said that the configuration should look like this to get https working:

[server]
PROTOCOL  = https
ROOT_URL  = https://git.example.com:3000/
HTTP_PORT = 3000
CERT_FILE = cert.pem
KEY_FILE  = key.pem

Then it took me quite a while to get it working until I realized that the values for the CERT_FILE and KEY_FILE should be absolute paths instead of the literal relative path.