Hi Kingoftheworld
I'm not sure that the Seine would be a particularly picturesque route, certainly not as you approach Paris and liable to be traffic laden. Unless you know it to be well served by cycle paths and minor roads, my instinct would be to avoid the Seine either side of Paris or any major cities such as Rouen and Le Havre as long stretches are likely to make for uncomfortable/unpleasant cycling.
A lot of cyclists seem quite content to cycle along easily avoidable major roads, which to my mind defeats the whole purpose of cycle touring, not to mention being quite dangerous.
If your really looking to get the most out of your journey across France, I'd buy a Michelin road atlas of france (£8/9) and tear out relevant pages for your actual trip. It's sufficiently detailed to identify more rewarding rural backroads and picturesque routes are clearly marked in green - planning accordingly has generally served me well. I'm fairly certain that with a bit of additional research, you could generate a much more rewarding route.
Best of luck with your trip, look forward to hearing about it.