"Muz z prvního století", a.k.a "The Man from the First Century", a.k.a "Man in Outer Space" (1962)
"A workman is accidentally sent into outer space, where he meets an alien that can make himself invisible. They return to Earth in the year 2447. Complications ensue."
It is a movie from Czechoslovakia, it is from the 60's and it has an invisible alien. Here you can find some screenshoots from the movie:
Here is a long clip:
Early in the clip, at 0:12:13, and near the end of the clip, at 1:04:18 you can see people floating in a room.
I am pretty sure this is your movie. If you agree, please select my answer as Best Answer by clicking on the yellow star next to it.
Pictures of those floating people: