I understand that "blocks" aren't really a thing in France.
What is the normal way to tell someone to "take the third right" or "go three blocks, then turn right" in French?
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In France, when giving directions, we count intersections (carrefour). Furthermore, because cities are rarely on a grid and it can sometimes be difficult to tell a low-traffic side street from a driveway, we're a bit more likely to give more details about the nature of the intersection than in the US.
Prenez la troisième à droite. (Take the third right.)
Prenez la troisième rue à droite. (Take the third right.)
Prenez la prochaine (rue) à droite. (Take the next right.) (commonly said by humans)
Tournez à droite au prochain carrefour. (Take the next right.) (commonly said by humans)
Au carrefour, tournez à droite. (Take the next right.) (commonly used by GPS)
Tournez à droite au prochain feu. (Turn right at the next lights.)
Tournez à droite au rond-point. (Turn right at the roundabout.)
Continuez tout droit jusqu'au stop, puis tournez à droite. (Go straight until the stop sign, then turn right.)
I haven't lived in Québec, but a Google search finds the same expressions on Québec sites, so I think there's no difference.
The literal translation of “block” in this sense is pâté (de maisons) but it would never be used when giving directions, only in expressions like “going round the block” (“faire le tour du pâté de maisons”).
Similarly, we rarely use blocks to express distances, nor intersections, because without a grid layout, those aren't really meaningful. We either give distances in meters or kilometers, or
Nous habitons sur le même pâté de maisons. (We live on the same block.)
La boulangerie est de l'autre côté de la rue. (The bakery is on the opposite side of the street.)
La boucherie est à cinq cents mètres. (Where in the US you might say the butcher's is two blocks away.)
Le supermarché est à trois kilomètres / à cinq minutes en voiture. (The supermarket is two miles away / five minutes' drive away.)
La gare est à un kilomètre / à dix minutes à pieds. (The station is half a mile / ten minutes' walk away)