There are two options I would consider;
Firstly, is it likely that your covering letter and C.V. will be appropriate and relevant for both your internship application, and permanent employment? If not, then simply include another CV and covering letter for James to distribute to colleagues - in which case, you can use Dear Sir/madam, or to who it may concern on that version.
If the same covering letter and C.V. would be relevant for both types of position,
I would personally still address it just to James, therefore 'Dear James' and then in the covering letter you might add a small thank you or mention for passing it to other staff for consideration of permanent employment which they will read. If he is personally sending it to other staff members, they may reasonably expect it to have just been addressed to him anyway.