I'm not sure why you think it's set in the 'present'. There's a lot of stuff apart from the cars that suggest the setting is several decades ago. I don't think they had a specific date in mind, just vaguely past time.
The very first shot was a TV set that looked something like this,
and had a black and white picture, typical of th 1960's
Linguini had a fridge in his home that looked something like this, typical of the 1960's
The restaurant had a phone that looked like this, typical of the 1950s:
Ego used an old manual typewriter.
Collete punched in on a mechanical timeclock.
Roller skates rather than roller blades.
Old fashioned lamp posts.
Nobody has a mobile phone.
The most modern looking object in the film was a push-button payphone.
Even DNA paternity testing was available from the 1960's. Not sure if it could be done from a single hair, but let's not quibble about such details in a film about a talking rat.