Yes we went to Paris one year for final stage. Wonderful experience. People do start to nab their spot pretty early. We walked down Champs Élysées at 10 am and it was already 5 deep in places. Eventually we found a spot at the front of the barrier on the Rue de Rivoli. It was quieter there than most other areas.
Don't forget that after the race all the teams do a lap of honour on the Champs élysées . We didn't realise this at the time but found a great spot as we were walking back to our hotel. Lots of photo opportunities.
We are going to the Alpe D'Huez stage the day before Paris and I can't wait. Hope you have a great time