Does this carbon fork have a crack in it that would make you replace it?

It looks like just a paint scrape to me. You should be ok. That said, some stranger over the Internet can’t make this judgment call for you - do you feel secure riding it?

What is visible in the photo is a paint scratch. Letting the bike simply fall over will not structurally damage carbon fiber composite. People seem to think CFC is fragile but it’s really quite robust.

The fact that you had a collision is much more worrying. How hard? At what angle?

Hard, head-on collisions can certainly damage the frame or fork. The stresses are higher in the head tube or steerer area as the fork acts like a lever. Often damage to the head tube can occur but the fork is un- (or less) damaged.

Strangers on the internet, no matter how knowledgeable or well intentioned, will not be able to diagnose internal damage to any part, no matter what it's made of.

Your local bike shop may be able to diagnose it.

For real confidence, find a local frame builder, preferably one who works in carbon fiber and pay to have it inspected. Yes, pay. He's a professional and makes her living this way, and you want quality advice, since it's your neck on the line. The advice in this answer I wrote a while ago, though addressing a steel frame and head-tube damage, applies equally to your potential fork damage.

See also this and this.

No, I'm not a frame builder, but I did know one when I was a kid. He spent many years in school and many, many years perfecting his craft. He took immense pride in his work and letting something out of his shop that he felt was dangerous was something he would not do. After finding that same attitude and level of pride with the builder who examined my frame after my wreck in college, I can't imagine a single frame builder who would do different.