Aside from the code aspect, which has already been answered, you also need to consider the I/O aspect of accessing the file.
A note on architecture and how I have completed this task in the past - not suggesting that this is the one right approach or that it is necessarily appropriate for your application. However, I thought my notes might be helpful for your thought process:
Set up a ManualResetEvent field, call it ActivateReader or something similar, this will become more obvious further on. Initialize it as false.
Set up a boolean field, call it TerminateReaderThread. Initialize it as false, again this will become more obvious further on.
Set up a Queue<string> field, call it Files and initialize it.
My main application thread checks to see if there's a lock on the files queue before writing each of the relevant file paths into it. Once the file's been written, the reset event is tripped indicating to the queue reader thread that there are unread files in the queue.
I then set up a thread to act as a queue reader. This thread waits for the ManualResetEvent to be tripped using the WaitAny() method - this is a blocking method that unblocks once the ManualResetEvent is tripped. Once it is tripped, the thread checks to see if a thread shutdown has been initiated [by checking the TerminateReaderThread field]. If a shutdown has been initiated, the thread shuts down gracefully, otherwise it reads the next item from the queue and spawns a worker thread to process the file. I then lock the queue before checking to see if there's any items left. If no items are left, I reset the ManualResetEvent which will pause our thread on the next go-around. I then unlock the queue so the main thread can continue writing to it.
Each instance of the worker thread attempts to gain an exclusive lock on the file it was initiated with until some timeout elapses, if the lock is successful, it processes the file, if it's unsuccessful, it either retries as necessary, throws an exception and terminates itself. In the event of an exception, the thread can add the file to the end of the queue so another thread can pick it up again at a later point. Be aware that if you do this, then you need to consider the endless loop an I/O read issue could cause. In such an event a dictionary of failed files with counters of how many times they've failed could be useful so that if some limit was reached you could cease to re-add the file to the end of the queue.
Once my application decides the reader thread is no longer needed, it sets the TerminateReaderThread field to true. Next time the reader thread cycles to the start of its process, its shutdown process will be activated.