To friend vs. to befriend
Friend as a verb is very old, but its use is now limited to adding someone to a list of social network contacts. Befriend doesn’t necessarily mean ‘make a friend of’. It is typically used when a person offers support to someone in difficulties, rather like the good Samaritan.
If you’re describing the establishment of a close, but not sexual or romantic, relationship, you have to say that two people are, or have become, friends.