The second syllable has the clue, here is how to bill and coo…

This soft word can mean to whisper sweet nothings, or if you’re less sentimental, you can use it to dismiss a singer as a mere crooner.  It can also evoke the cooing of a bird.

The business of billing and cooing, or just cooing, is ‘la roucoulade’ and an individual example is ‘le roucoulement’ (I think I have the distinction between these two nouns right).