I've not had problems importing AVCHD from a couple of (different) Canon Camcorders I have using FCE 4.1 running on Yosemite; I use the Log Transfer window to bring those files in. I've not upgraded to El Capitan - I plan to wait for the dust to settle before doing that. .
One other thing I sometimes do is import the files into either iMovie or iSkysoft Video Converter. The latter does the job but for long videos (~20+ min), loses audio-video sync, which may be related to the Merge Video option; still working on figuring that out. The former, you have to go hunting for the files inside the library by Show Package Contents.
One useful tip: if you import by non-FCE means, I recommend opening the newly imported files in MPEG Streamclip and then exporting them using Apple Intermediate Codec. That way, you don't have to render the movie files in FCE every time you make a small change (very annoying!), which you have to do in any other format.
Good luck.