doesn't it mean that most of their arrows would just collide with the trees?

Forests aren't dense impenetrable biomes. Of course it would be ridiculous for an entire army to put their archers in the middle of a wood and expect them to shoot through the leaves. More likely, the archers were deployed at the edge of the forest where they had a clear line of sight. English archers were known to have fought from relatively close distances (150m being the approximate effective range, and direct shooting was under 30m). Clearly, if you're in a woodland, you'll find the best position to shoot from. If you're standing behind a tree, you probably wouldn't be a good archer.

The source you linked does indeed show the archers positioned on the edges of the forest.

What did French army do while they were building them up?

They were also forming up. The French had a fairly large army and it takes time to array the army into a battle formation. The English had the advantage of choosing the ground to fight on as they were on the defensive. I don't know about your eyesight, but I imagine spotting a blob of soldiers putting up pointy sticks hundreds of metres of away isn't the most obvious thing you'd look for.

Even if they did see this, what would they do? Open the battle right away and walk into the prepared position that was meant to thwart them?