Doing touristy things in Paris will always be crowded especially in the summer, make your sightseeing reservations ahead of time. I don't believe the Olympics will have any impact on Frances traffic. I'm also of the "do it now rather than later" mindset like some of the other replies. If the bulk of your time will be spent on the Camino I'd just suck it up and deal with the crowds in Paris for the short term, but make your plans and reservations well ahead. Concerning lodging in Paris, the Basilique du Sacré-Cœur de Montmartre runs a guesthouse for stays up to 5 days. 15 euro for a bed in the dorm, 35 euro for a shared room, 40 euro for a single room (full or half pension also available), might be an interesting option for you considering you'll be going on pilgrimage afterwards. IMO what you want to do is feasible if you plan ahead.