Soizic,
There's nothing out of the ordinary in your log. The Preview window's size and position is stored in a file called "com.camerabits.PhotoMechanic.plist" and it is in the Preferences folder inside your Library folder.
Start by quitting Photo Mechanic Plus if it is currently open.
That file can be deleted and it will be created again by the system. I get to that location by opening a Finder window and then using the "Go to Folder..." command on the "Go" menu. This will likely be different on your French system.
A dialog will appear with a text field in it. Enter:
~/Library/Preferences
Then click the "Go" button. Find the com.camerabits.PhotoMechanic.plist file and rename it (or you can delete it, but renaming will let you get the file back if a new file doesn't help) by prefixing an 'x' to it (xcom.camerabits.PhotoMechanic.plist is what it should look like).
Start Photo Mechanic Plus again and set your Preview window size and position the way you like it. Restart Photo Mechanic Plus, open the Preview window again. Does it work correctly now?
HTH,
-Kirk