Rebshidduch, the question is getting more interesting. Are you saying that by not giving this guy a ride on grounds of tznius, he will feel insulted and it will reinforce a negative attitude towards being frum?
Or are you saying that the ride is to bring him to a kiruv event so he can find his way back?
So much of this depends on who the female and male in question are, what sort of interaction they will have in the car, what the purpose of the ride is, how frequent the ride will be (one time occurrence or regular car-pool), who else is in the car…
A female 30ish mother giving a ride to a rosh yeshiva, is not the same as a 20 yr old college student giving a ride to a fellow college student, is not the same as a female kiruv professional giving a ride to an OTD young man.
my opinion- if he must get to where the female driver is going, and this is the only safe/reasonable way to get there, and it is not going to be something regular, then he should sit in the back, and the driver should play some music or a shiur loudly to discourage conversation. And to address Froggie’s point, considering there is a high-backed seat between him and the driver, he won’t be able to see her from the back – it’s not like walking behind her on a street or sitting behind her on a bus where he would see her walk on/off.