From my... thoughts(?), the contraction is between the two vowels sounding. In French, with 'Le' and the phonetic of hombre, it would make sense. But in Spanish, you have 'el' with the 'L' sound separating the 'Eh' and 'Oh' sounds of the two words.
Beber is the verb to drink now depending on the situation The man drinks is el hombre bebe and usually refers to alcohol drinking. Now if after the Bebe you use a drink or something liquid then it refers that he drinks that particular drink.