From a contemporary perspective, "Julie" may seem slightly more reasonable than its counterpart, as it does exist in Sweden as a female first name that parents would give to their daughter. However, I don't believe it is a Swedish name in origin. And this graph also tells us its usage previous to 2000 was vanishingly sparse, much less one and a half centuries ago. It had not appeared in non-French literary works either until Miss Julie came along.
The first appearance of Julie in a popular non-French literary work occurred with Swedish playwright August Strindberg's tragedy Miss Julie in 1888. As it became one of the most widely performed plays in the English-speaking world, the choice of Julie as a name expanded along with it. (Wikipedia)
The choice of "Jean" is a bigger mystery: it is obviously a French name, popular in French speaking regions. However, the name has never had any kind of popularity in Sweden that could be spoken of. The character Jean is a local peasant boy hoping to climb up the social ladder and take some short cuts while doing it.
Why did August Strindberg choose these two names? French influence? Even so I imagine he'd have had allusions and literary references in mind when making these choices as these names were minusculely rare if at all existent back in his day.