We used to say "petit ami" and "petit copain", but there are a little aged now. "Petit ami" is fine if you're talking to your parents or older, but "petit copain" sound reaaaally old.
"Petit copain" became "copain". "Ami" still means friend. "Mec" is also used a lot.
It sounds like it's hard to tell the difference between friend and boyfriend but really it isn't :
Je suis venue avec mon copain vs Je suis venue avec un copain/pote
(I came with my boyfriend vs I came with a friend (of mine, implicitly)
J'ai croisé un mec dans la rue vs J'ai croisé mon mec dans la rue
(I bumped into a guy in the street vs I bumped into my boyfriend in the street)
Basically, it's the possession that tells "boyfriend" apart from "friend". See also :
J'ai un mec
(I have a boyfriend, marks possession as well)
The same applies for "girlfirend" : "Copine" is the most common, "petite amie" is dated but not that bad, and the "equivalent" of "mec" is "meuf", but it's a little more casual and vulgar, don't use it with anyone.