Translation:The woman is drinking a beer and the man a coffee.
The repetition wouldn't sound natural in English and it seems French speakers would agree; it's common to omit the second instance of the verb in sentences like this. This doesn't really indicate a grammar rule specific to French; it's a general appreciation of realistic speech patterns across languages with similar syntax (e.g. English and French).
Lyn576698 is right about that being common usage in English. It's technically called ellipsis (meaning grammatical ellipsis, not the three spaced dots), in which the verb of one phrase is understood to carry over to the second phrase.
Many English speakers would punctuate to help indicate ellipsis (though that trend is dwindling): The woman is drinking a beer and the man, a coffee.