This is a translation of the French imperfect past tense - which has no direct English equivalent. “Would hear” may be an attempt to concisely match the French imparfait in describing an event occurring repeatedly, with uncertain frequency and timing, and the speakers ‘doubt’ now that a monster was really ever “heard”.

“Heard” could have been used - as there are few absolute rules in translation - but ‘would hear’ is a very good fit.  

Of course, the decision could also have been made because 3 syllables were needed in English to match the French phrase ! 

You can find all the listening exercises here: French-listening-practice

You can do a text search (ctrl + f) on that page for "song". 

The one you're thinking of is by Zaz - "On ira" which is one of my favourites. 

I'd also recommend the Keren Ann and Lynda Lemay songs.

Merci beaucoup!