They say you are each in love with this museum (6)
I believe the answer is:
louvre
'this museum' is the definition.
(art museum in Paris)
I cannot understand how the rest of the clue works.
(Other definitions for louvre that I've seen before include "Famous Paris national gallery of art" , "Great art gallery in Paris" , "Type of windows and doors" , "European museum" , "Great art museum-gallery in Paris" .)