final cut express HD 4.0.1 and OS X 10.9.5 with AVCHD

Well, the news is probably not what you want to hear. FCE was discontinued over 3 years ago, even before Lion (10.7) was released. FCE 4.0.1 was the final update to FCE. There is no guarantee that FCE will work well, or at all, on Lion, Mt. Lion or Mavericks.

If you already had FCE installed on your Mac, and then upgraded to Mavericks, that could be source of the problem. Pro apps, like FCE, generally need to be reinstalled after upgrading the OS. That leads to another challenge (problem) which is installing FCE on Mavericks. The FCE installer is an old PPC app and without Rosetta support it won't run on Mavericks. I'd be very careful about trying to uninstall/reinstall FCE on Mavericks. (Research it thoroughly, and you may even need to resort to using Pacifistto install FCE on Mavericks - it's a complex process.)

It might be worth trashing the preferences as it occasionally works miracles when FCE misbehaves.

Download this free app.

http://www.digitalrebellion.com/prefman/

Shut down FCE, open PreferenceManager and in the window that appears:-

1. Ensure that FCE is selected.

2. Click Trash

The job is done instantly and you can re-open FCE.

You could be right but it only takes a minute to download and trash the preferences.

Trashing the preferences should be the first thing you do whenever FCE starts behaving strangely in any way.

You should do it if only to remove it from the list of suspects.

Over the years I have occasionally had problems which have lasted for days because I thought they couldn't possibly be caused by corrupt preferences . . . . .

Mavericks does not show the AVCHD contents when you double click it.

You need to control-click and select "Show Contents" and keep doing this until the video .MTS files are revealed.