Final Cut Pro 7 (and any

Final Cut Pro 7 (and any previous version) does not have native editing support for AVCHD footage. When working with AVCHD recordings in Final Cut Pro, the first thing you need to do is ingesting AVCHD in the Log and Transfer window, where you transcode H.264/AVC to an Apple ProRes codec or the Apple Intermediate Codec, both are natively supported by Final Cut Pro.

Source: http://www.brorsoft.com/how-to/get-final-cut-pro-work-with-individual-mts-m2ts-avchd-files.html