Learn French: Il n'y a pas de vent, mais je vois la fumée monter. - There is no wind, but I see the smoke rising.

In French, when you use a verb of perception like voir (to see) followed by an action, that second verb stays in the infinitive. While English often uses an "-ing" word for this continuous action, French simply uses the infinitive: je vois la fumée monter (literally, "I see the smoke to rise").

Could I change the word order and say je vois monter la fumée instead?

Yes! With verbs of perception, you can actually put the infinitive either after the object (je vois la fumée monter) or right before it (je vois monter la fumée). Both are correct and mean the exact same thing, though putting the object first is the most standard everyday structure.

Why is it pas de vent and not pas du vent?

This is a quick reminder of the negative article rule. In a positive sentence, you use the partitive article for uncountable things, like Il y a du vent (There is wind). But when a sentence is negative, partitive articles like du change to de. Therefore, it becomes Il n'y a pas de vent.

Doesn't monter usually mean "to climb"?

It often does, but monter more broadly means "to go up." Depending on the context, it can translate to "to climb" (like stairs or a hill), "to get in" (a car or train), or, as in this sentence, "to rise" (like smoke, heat, or water levels).