While in the military during the late sixties I saw a b&w movie involving a couple in love and had an argument during the relationship. They separated and while attempting to see each other to apologize, they were involved in an accident (possibly a head on collision)which ended with them dying and the movie changed by final narration was" this is not the way to end a love story." The real ending was showing them getting back together and getting married

Help Please... I can't think anymore!!

Maybe "A Man and a Woman" (French film)