Met
Jet streams are related to cold/warm fronts. You cannot per say have a front without a Jet stream. This question tries to make it more complicated by saying that you cross a jet stream at right angles instead of just saying that you are going through a cold front.
A cold front is a HIGH pressure area. High pressure has clockwise movement. If you draw a picture of a HIGH and a plane flying through it you can tell which way the wind will blow you.
I'm not a 100% sure but it would seem to me that you'd be blown to the left (port).
I might be wrong and you might actually be going over a Warm front. In that case the answer would change to starboard drift.
Sorry.