Romance movie set in Paris. American man with French woman

I saw about the first 20 minutes of this movie years ago. It looked amusing and I want to see how it plays out.
The story: two strangers, Paris: an older American man and a beautiful younger girl. They both board a bus? (train, definitely public transport). The police? board the bus and check for tickets. The woman did not buy a ticker. On impulse the man gives the woman his ticket and then the police speak to him. After this he spends all his time searching for her on buses.

That is when I stopped watching. I have a feeling the man was an author.

If anyone knows this movie I would enjoy watching it. Thanks.

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bitter moon 1992

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