The implication is that OP is reading a translation. Descartes likely used the word 'esprit', different translations may cause confusion around the word.

The answer is probably 'nearly'. Like, l'esprit may translate into 'the force which animates' - which could be mind or soul (I'm not a native french speaker - native speakers jump in!). This is sort of the difficultly in translation, l'esprit will have different connotations to a native speaker compared to mind/soul for an English speaker. The meaning is also going to be context sensitive for a given passage. When you're reading just keep in mind the translated words may have a broader connotation or a connotation that isn't native to you. English and French share a lot of roots though, so it's not so bad!