My suggestion would be to be about half-way down the Champs on the left looking towards l'Etoile (i.e. on the downhill side) - you'll get a good view as they pass going up the hill on the other side and then as they whiz past on the downhill - as well as seeing the finish line down the hill to your right. I watched Armstrong's fifth "win" from there. (There's a McDonalds for toilets IIRC)
The other option is at the Place de la Concorde end, same side, on the corner when you'll see them come from the Rue de Rivoli into the Champs - and also see the action on the giant screen.
As suggested get there a good 5-6 hours ahead of the start of the circuits
I have to own up to having been by invitation to the grandstand ("Tribune") area by the finish line a couple of times including 2013 when they had the late evening finish and fireworks - an amazing experience.
Post-finish is you're of a mind you can walk in among all the team buses parked in the corner of the Place de la Concorde outside the Hotel de Crillon and see bikes, riders, team cars etc. All pretty informal.
Rob
PS - The publicity caravan goes past but doesn't chuck out the freebies - some of the caravan float staff are clearly demob-happy and dancing topless women aren't an unusual sight as they drive past. AND spare a thought for the bloke in driving the Credit Lyonnais lion (stuffed, on a quad bike) after 3,000 km in rain or shine - I'd like to do that!