“À travers le monde” is correct only when you imply a search action:

“Il a cherché sa femme partout à travers le monde” –> He searched for his wife all over the world

I would rather suggest “dans le monde entier”, even though “à travers le monde” is the correct literal translation.

There is an older and more refined expression, de par le monde.

It’s not usable in all contexts, but if you intend to say “They travelled throughout the world”, then a good translation (for a higher language register) is “Elles ont voyagé de par le monde” (although “à travers le monde”, “dans le monde entier”, “partout dans le monde”) are also OK.