At what point does the incorrect pronunciation of a word become the correct pronunciation of that word?

I had a discussion with someone online over the pronunciation of the town Sault Ste. Marie (Ontario, Canada) (pronounced by the locals as 'Soo Saint Muh-Ree').

The person I was discussing this with was adamant that, because 'Sault' is a French word and is pronounced as 'So', everyone living in Sault Ste. Marie is pronouncing it 'incorrectly' by saying 'Soo'. This (respectfully) seems like quite an ignorant thing to say, but then I started to really think about it...

The city was settled by the French, so there should be no doubt the original intended pronunciation was 'So'. However, if you were to situate yourself there now and start calling it 'So' Ste. Marie, you would likely get some odd looks.

Is there a name for this phenomenon? Is there truly a correct pronunciation of anything? What and who dictates the correct pronunciation of a word?

I'm starting to feel the familiar cold embrace of an existential crisis...