To send your public key by email in Mailfence web-interface:
1. Go to your Messages and click on New.
2. Go to Attachment (in right section) and click on Attach my public key.
For this option to appear, OpenPGP key pair must exist (generate/import) and associated with the respective sender address.
You can additionally always Digitally sign the email message with the respective OpenPGP private key, to assure the recipient that you are indeed the owner of that OpenPGP key pair.
Some of the other ways of exchanging OpenPGP public key can be found in this blogpost.