The way my schedule looks now, I will have a free period senior year from finishing Chinese as a junior. I am currently a sophomore, so a lot could change in the meantime, but I wanted to get you guys’ thoughts about whether it is feasible to take US or Euro and World concurrently.
Have you taken AP courses before? If you understand the time commitments of AP’s and it’s an area that interests you, it should be fine. I would check with your guidance counselor just to be sure there aren’t any restrictions, some schools handle AP’s differently.
It should be feasible, but I agree with the commenter above that you should probably have some experience in AP classes. And just make sure you enjoy the subject and aren’t just taking it to get another AP credit. 
Have you taken AP classes before?
Why AP History in particular?
I would be wary of pairing AP World with APUSH, as both are very large content-wise.
I would only suggest doing that if you really love history.
Not only is it feasible, I actually think doing AP Euro and AP World at the same time should be recommended.
The content they go through often overlaps. You end up doing many things in AP Euro and then going through it again in World (there is a lot of European stuff in World). For example, the reformation was covered in Euro and I found it extremely easy when it was covered in World.
As long as you study hard in Euro, second semester for World should be a breeze if you studied hard during Euro. Honestly, it’s probably one of the best AP combinations (other than CompGov+Gov).
The content DOES NOT overlap, except in minor ways toward the end. Ap world starts in prehistory and moves through various Ancient and Iron age civilizations; during that time, AP euro is focusing on things happening 2,000 years later, in the renaissance then the age of absolutism. The timelines never connect. In addition, they purposely cover different geographical areas. The first semester has zero content overlap. When you get to the second semester of AP world, you start crossing ideas that were presented at the beginning of Ap euro, but you cover different angles (IE., how the renaissance impacted the Americas vs. How it impacted Europe) or you may come across one European example among five different examples (for instance you’d have examples from the Ottoman empire, India, China, Japan, and Europe so just a very small part of a chapter on the total…)
However I agree that since the 2016 edition all formats match so if you took AP human geography you have a basic idea of the approach, then if you take AP euro you’ll have a good handle on the AP exam format for world, and vice versa. Thus, I would take them consecutively not together.