The couple moved out after missing so much sleep that the woman's health was suffering, they told city's administrative court on Thursday.
Now they are claiming €8,500 in damages.
The couple said the second-floor flat was rented to them as a particularly quiet one – and that they were not told about the man living upstairs.
It was only after they moved in last April that they discovered that the man upstairs snored so loudly they could not sleep.
The judge said it was not enough simply to say that he snored every night, and asked the couple to produce a snore diary of the nights they had been disturbed.
The case continues.