H.264 isn't really an editing format. It is a delivery codec...final output, because it is highly compressed FCP will try, but will struggle. Avid might totally freeze up. Handbrake won't make things better.
Adobe Premiere will work with the files, but really only if you have a beefy computer and a graphics card that is powerful and is CUDA enabled to enable the MERCURY ENGINE in Premiere. Because, again, this is a complex and highly compressed format.
If you want to use footage in Avid Media Composer, you will need to transcode it to an Avid format. AMA to bring it in, then transcode...or IMPORT and transcode. DNxHD if this is an HD size H.264. 2:1 MXF if this is an SD format.
Shane
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