This reminded me of:
The Great Race, also 1965
A period comedy wherein a competition is announced to race autos from New York to Paris. Tony Curtis, Jack Lemmon, Natalie Wood (yum), Peter Falk, Ross Martin on loan from The Wild, Wild West, the longest and pie-iest pie fight on film (at the time, anyway), music by Henry Mancini, all directed by Blake Edwards. One of my favorite movies of all time.