Ford Prefect has been stranded on earth for fifteen years, which leaves about nine years before he was saved by and met Arthur. How, in those nine years, did he not realize that cars weren't the dominant species on earth?
The incident you describe only exists in the film, not in the original radio series or the books.
When Ford came to Earth he knew so little about it that he chose the name "Ford Prefect" as he thought it would be "nicely inconspicuous". This isn't because he thought that cars were the dominant species but simply that it was a common name.
The fact that the Ford Motor Company had discontinued the Prefect model years before is irrelevant to the story. The name just scans well for the humour of the story.
The scene in the film is just a visual key while the voiceover is repeating the quotation from the radio and books about the name being common. The car in the film is indeed a 1960s Ford Prefect.
This is an older question but I'll attempt an answer anyway.
In the books, Arthur refers back to when he first met Ford and says something along the lines of "When you first got here, you thought cars were the dominant life form!"
This assumption was probably because there are a lot of them, they move, they are everywhere, the whole world is formed around being accessible to cars, and any number of other reasons (this is not spelled out in the book, but if an alien was to first visit Earth I wouldn't think it was a strange assumption.)
Ford was merely trying to introduce himself to what he incorrectly thought was a sentient being, and the dominant lifeform. A "Take me to your leader!" type deal. It was only afterwards that he realised humans are the dominant lifeform and not just servants of the car 'master race'.
EDIT: I agree with the above answer that the actual 'introducing himself' scene was nowhere to be found. But iirc the statement about cars being the dominant life form was there.