Was the vfat partition mounted after the nfs server started? If you put an entry in /etc/fstab, you should be able to share it.
Also, watch the options when you mount the vfat filesystem. Fat32 doesn't contain Linux inodes so you need to determine the ownership and permissions of the entire drive en mass. All of the files will have the same permissions. All of the directories will have the same permissions.
Read the man page for the mount command. The uid, and gid options affect who the owner and group of the filesystem is. The fmask and dmask options determine what the rights are.
If this isn't a removable device, and you aren't dual booting, don't use a vfat filesystem. If it is an external drive, but you don't move it to a Windows machine, it would make sense to reformat it using a native linux filesystem such as ext3 or xfs.