FCP is a limited audio tool. Sound track Pro is better.
The basic characteristic of getting that ‘next door’ sound from a clean recording is the combination of EQ and room reverb.
Walls attenuate high frequencies so you want an EQ that shelves off the hi frequencies above 2khz. Also play with bass frequencies. It might sound more natural to roll off low frequencies but add a bump around 400hz
The dialog also needs reverb – not a big cathedral sound but a tight live room. Again STP is more likely to have the reverb tools to do this. Although I have FCP I also have Fairlight with VST plugins and convolution reverbs so this sort of thing is a piece of cake, but not easy in FCP.