Also known as Naked Under Leather, it was a 1968 British-French film starring Marianne Faithfull and Alain Delon (who was once called "the male Bridget Bardot"). The film also featured Roger Mutton, Marius Goring, and Catherine Jourdan.
Originally filming was wrapped-up in time to compete at the 1968 Cannes Film Festival, but the festival was canceled due to the largest general strike ever attempted in France, and the first ever nation-wide wildcat general strike in May of 1968.
The Girl on a Motorcycle is probably best remembered for the leather jacket/full body suit (see Emma Peel) that Marianne Faithfull wore in the film.
In a nut-shell, the plot is new-bride Rebecca leaves her husband's Alsatian bed on her prized motorcycle (a 1967 Harley-Davidson FL was used)—her symbol of freedom and escape—to visit her lover, Daniel, in Heidelberg. On her way she indulges in psychedelic and erotic reveries as she relives her changing relationship with the two men, before crashing into a truck at the film's conclusion.