> What are the mechanics of how this works? If I agree to buy a property for a million dollars, does the city get a chance to match that price?

there's a French wiki page on this: https://fr.wikipedia.org/wiki/Droit_de_pr%C3%A9emption_urbai...

But basically, yes, the city has 2 months to match the price. The city can also offer a lower price, which can be refused (so no sale at all) or can be argued in front of a special judge, who'd rule if the price offered by the city is acceptable, depending on the local housing market.

It's not a rule that's specific to Paris, but which is applicable in most French cities.