Please check out the explanation in the mount man page: https://manpages.debian.org/bullseye/mount/mount.8.en.html#Non-superuser_mounts
Hence in /etc/fstab, add the ,user to the mount options, then I probably sudo systemctl daemon-reload is required to reload it. Then try again as unprivileged user.
… ah wait, I think I misunderstood, you want to mount it as unprivileged user on macOS. Generally since it is UNIX as well, the same may work on macOS as well, but not sure. But this is not something that can be controlled server-wise, instead it needs to be configured on the client system (macOS).
… ah and misunderstood another thing 
, not mounting the drive as unprivileged user is the issue, but writing files in the mount point. Try to change the mode either on the server or on macOS (as root): sudo chmod -R 0777 /Users/cmoullia/private/nfs
You can also change the owner:group, sudo chown -R root:root /Users/cmoullia/private/nfs
With 0777 mode the owner doesn’t matter, but root is assured to be UID 0 and GID on both systems, with every other user it is possible that it doesn’t exist on one end. As alternative you can create the macOS user at the server with the same UID, like: useradd -u 1234 cmoullia