According to the Atlantic, a spokesman for the network did not respond as to whether or not it considers the moon landing a potential conspiracy. The Atlantic also notes that this is not Fox's first time questioning the veracity of NASA's claims.
One ought not be too surprised that Fox News would insinuate the moon landing could have been a hoax, considering its willingness to openly promulgate other conspiracies:
It seemed to confirm that Fox occasionally caters to the fringe. But the same network also amplified a poorly sourced conspiracy theory about Seth Rich, a murdered Democratic staffer, for weeks, before suddenly abandoning the story. Other journalists from the network have misreported stories about climate change and asked how global warming can be real if it also sometimes snows.