I went the year Landis "won" it - crowds were well down on the year before due to other drugs rumpuses so getting there an hour early meant we got a good view - IIRC about 400m up the Champs Elysee from the Pl de la Concorde. No idea if numbers have picked up again.
Make a weekend of it. I went with the family - my son keen on cycling, wife and daughter not, but while we grabbed a decent position, they went for a bit of window shopping and joined us during the race and enjoyed the atmosphere. Like London, Paris is so big that even the TDF does not cause hotel and travel prices to rise, so we got a fairly good deal on both.