Ok so I've listened to various videos from Francophone media of Québec, and all of them do pronounce the final -re (which the Anglophones don't), probably because the name is too close to the word lièvre not to pronounce the final -re, most also pronounced the "i" in "lièvre" as a semi-vowel and not the full "ee" English vowel (except one guy, MP Joël Godin, who pronounced it like English "ee"), but half of them seem to say "
Polièvre", under English influence I suppose, while another half say "
Poilièvre". For example the mayor of Montréal (at 0:25) definitely says Po- and not Poi-.
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On the other hand this journalist clearly says Poi- :
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So, the jury is out on how to pronounce his name in French it seems.
In France it will be fully pronounced Poids - lièvre, I'm sure.
As a matter of fact (at 1:09). Notice how the "Poi" is very neatly pronounced, and the final -re is also much more forceful than in those Québéc videos above.
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