Most browsers do not allow default values in File fields for security reasons.

Also, you can use alternate quoting methods so that you don't have to escape the double quotes.
Here are just two examples:

$field = qq{<input type="file" name="pic" value="$fields[2]">};

or 

$field = "<input type='file' name='pic' value='$fields[2]'>";
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Clayton --
Clayton