I don't see a problem with the phrase "closed source". "Closed" means "not open". The opposite of "the door is open" is "the door is closed", not, "the door is close". Similarly, there is "open mind" and "closed mind", etc. ("Close" can also mean "nearby", which is not the intended meaning here.)
One of the definitions for closed in Collins is "restricted; exclusive". When we accept this definition, "closed-source software" is software where access to the source code is restricted to those who own the code's copyright (or that subset of employees who actually contribute to it).
Another definition from Collins is "blocked against entry; shut". Closed-source software is kept in source code repositories that block access from the outside world.
"Opened" would assume that the source code was previously "closed". You can find instances of the phrase opened source software on the web, but it is not clear whether it always refers to software that was previously proprietary. The phrase "open-source software" is more common.