2 suggestions.
1: the quick fix
One your file in quicktikmeplayer
Open... can't remember the window's name but command j will open it
Select video track , Visual settings, and there's a check box or two for instant de-interlacing.
2: slower
Export your file, bring it back into FCP
Apply a de-interlace filter, and render.
Rendering in fcp should be safer as you don't need to do the whole film in one go,
You can stop and start, although I've never found I needed to.
3: slower and better
Use the Graeme Nattress smart de-interlace
This 3rd party plug in will give you the best de-interlaceing possible in FCP
4: compressor settings
Are the frame controls set to best?
That will take forever (and i've heard can also leave you with unwanted artefacts)
Sert them to better
Nick