It is an old movie (if I’m not mistaken 90s movie). The plot is about a successful woman (maybe a lawyer) that one day takes a taxi ride. After she gets off the offers the cabbie to accompany here to some sort of event. As the movie goes on she fall in love with him. The cabbie is bearded with bad manners, but during the movie he shaves his beard and try to fit here lifestyle.
Minnie and Moskowitz is not exactly what you describe (make in 1970s, the man is a car parking attendant, and woman is a museum curator), but the plot is similar. http://www.imdb.com/title/tt0067433/?ref_=nm_flmg_act_59
Fall (1997)
http://www.imdb.com/title/tt0119098/
Or Nick and Jane (1997)
It is Nick and Jane.
Thank you ChickHabit !
This one is solved.
No thank you you Alejandro for actually confirming a solve, its been a while.
Thanks ChickHabit!