Well we can't have this topic if someone doesn't mention Harry Turtledove's "World War" series. A big part of that is thought the aliens have late 90s tech levels, they don't have the supplies to maintain combat against all the nations at once. That actually seems to be close to X-com as we know it, with infiltrators and terror rather than outright combat.
Perhaps instead of shooting down the crafts, the radar coverage is your spy network, and you have to wait for the machine to land. However, the aliens stay on the ground longer, and X-com has bigger forces to deal with the higher alien population. Kevlar is still a few decades away so no body armor, and the only thing close to the HWPs would be the ineffective "Goliath" remote bomb used by Germany. Lasers are also a post war concept, so there wouldn't be much of a middle ground between human weapons and plasma.
Aside from the late war STG-44, there weren't really any select-fire rifles, so there would need to be a fairly clear difference between semi-auyo full powered weapons and sub-machineguns, with possible light MGs (m1919/mg-42) in the mix. This shouldn't be too hard to implement - rifles have snap or aimed only, smgs are snap or burst and lower damage, Machineguns fire burst, and use so many TUs that you can't move before shooting (ie 75-90%).
This might be some extra work, but we might want to consider making the story a little more than a rehash of what we know, just with different weapons. Perhaps these are creatures from Lemuria/hidden jungles in Antarctica. Rather than flying to Mars on 1940s tech, they head to the South Pole for the fianl mission of no return. (Functionally the same as Cydonia, just a palette swap.)
