El Capitan: Appstore says "downloaded" and "there's been an error" (stuck)
Apparently it downloaded the OS X El Capitan installation (under that name, or Install OS X El Capitan) in the Applications folder, which seems to be the download location. I could launch it from there. 

Problem solved…

UPDATE: if this would occur during you Mac OSX Sierra download, the file you'd be looking for is "(Install) macOS Sierra" in the Applications folder.