Out of interest, what exactly is the Periphique? How far in is it?
Is it the Paris equivalent of the north/south circular road but much more scary? Or is it the M25 equivalent, i.e. the A104 etc that links many of the main motorways eg A1/A4/A6 etc?
I would agree with the suggestion of keeping north of Paris, then dropping down via Rouen. On the other hand, if for any reason this does not appeal to you, the 'Francilienne' provides a very good alternative to the dreaded P