Given the task definition and input, reply with output. Given a travel related situation, and given a specific question about the situation, summarize the question into a title

Here's my situation. I am currently in France on an internship visa (different than a business and tourist visa) which ends next month. I'm interested in doing some traveling afterwards, ideally on a 90-day Schengen tourist visa. I'm willing to hop over to a non-Schengen country (like the UK) for a couple days and then come back to get the tourist visa if necessary.

This post seems similar to my question, except the OP is trying to get the tourist visa without leaving the Schengen area.

Is this allowed? Will the border patrol still give me the tourist visa after my internship visa expires? Will it work through the UK or should I go through another non-Schengen country? I have a USA passport.
Can I start a tourist Schengen visit after my long-term Schengen visa is over?