Here's what it means

Barbagal left when it was still dark,
with his cap on his eyes and riding a horse

With short pants and his two-litre bottle in hands
He shouted at the top of his voice "I'm a good for nothing"

Watching him run as if he had been a rat,
The dogs were mewing, the cats were barking

On the steeple at night he would make a racket
He shouted loud "The most handsome is me"

When the Monviso has its cap on (meaning there are clouds on top of the Monviso)
The weather will be bad or it will be fine.