"To bite the dust" apparently is:
"Biting the dust" is what happens when you fall face first into the dirt. It can mean a few things: for a person to die (though that would be a very crude way saying it - do not use at a funeral!), a machine to break, or in the case of the Queen song, for a competitor to lose/fall out of the competition. https://idioms.thefreedictionary.com/bites+the+dust
According to Word Reference, "mordre la poussière" means "to lose, to suffer a defeat" (https://www.wordreference.com/fren/mordre%20la%20poussi%C3%A8re). Can it also mean "to fail" and "to be killed", as the English idiom ?
The plosive 'b' and 'd' in English give the phrase urgency and violence, whereas the softer 'm' and particularly the '...oussiere' have the opposite effect. But I suppose with practice- I have, you can tell - you could sing this rhymically in time to Queen as as 'Un-au-tremord la-pouss-iere' whicjih is what they do 'An - oth - erone bites-the -dust'.