That's not really a decision for the US though, Europe's participation in Artemis is through the ESA.

I know Canada and Japan both have astronauts on early Artemis missions but I don't think its been decided who will be the first non-American to step on the Moon. That certainly won't happen on Artemis III but I bet it is a European given ESA's contributions. Will be an interesting and I assume hard fought over political decision when it does happen. Wouldn't surprise me if it did end up being a French astronaut though