What kind of car were they driving?

It's very possibly a 230 SL as the 250 SL came out in 1966, to be replaced in '67 by the 280 SL which was in production until 1971.

The white Benz was a 320SL (not a 230 or 250 which were five-seater 2-door hardtops) which had a removable rigid roof panel; in some of the in-car scenes look behind Hepburn's neck to see the left-hand chrome-plated roof panel release latch handle at the top of the interior beltline. I know it's a 320SL because back then I would have DIED to have owned one! - I had nearly every brochure that Benz distributed in the U.S. to promote the car. The 320SL was later superseded by the 350SL, which was later suppplanted by the 380SL - all looked quite alike, their differences being chiefly in uprated powerplants. Note the car's rigid roof panel is uniquely dished (concave) longitudinally (most cars' roofs are upwardly bulged - convex), the engineers at Daimler-Benz having incorporated the concavity following wind tunnel tests that showed this roofline acted, at speed, as a spoiler channeling airstream that produced a beneficial down-force on the car, thus improving road grip and stability.

For a brief spell the lead performers get a ride in a Citroen "deux c.v." - the arch-profiled, durable, redoubtable, popular - and agonizingly underpowered - French front-wheel-drive car powered by a two-cylinder engine. The BRG (British racing green) two-seater with the red grille louvres is indeed a hard-riding, spine-jarring MG-TD (MG being the marque/abbreviation of the maker's name: Morris Garages). The red two-seater convertible is indeed a Triumph Herald. At one point Hepburn hitches a ride in a gorgeous Alfa-Romeo GT (Gran Turismo), and after Finney catches her up on the roadway he speaks the marque's name.

It wasn't unusual for U.S. cars - in the instance of this film, the Ford station wagon - to be in France. In some of the Nouvelle Vague films they can be seen - usually driven by French hoods, as U.S. cars were associated in the French mind with swaggering American gangsters. Though in post-WWII days American cars were quite popular with the French, the much-higher cost of fuel there inhibited their numbers as U.S. cars were then, typically, gas-guzzlers.

Cars back then, like this delightful film, had CHARACTER! - no one needed to locate their badging to identify them: it's quite refreshing to enjoy seeing them in their out-of-the-showroom condition in vintage films. Unlike the "so-what?" sense one inevitably feels when gazing benumbedly upon today's mass of lookalike automotive wegdeblob clones.