Right you are! In fact, the last stage is always a formality (by tradition) with a few notable exceptions, such as in 1989, when it was an individual time trial. It’s generally considered poor form for a general-classification contender to attack on the last stage.
Not quite…2003 marked 100 years since the first Tour, so the riders did ten laps, not the usual eight.
I’m not sure how one gets from “we were there for hours” to “the peloton was slow.” Those ten laps took 80 minutes or so—maybe a little less.[sup]1[/sup]
Those not-particularly-speedy professional bicycle racers completed that day’s 152 kilometers in three hours and 39 minutes. That’s an average of about 41.6 km/h (25.8 mph).
I didn’t find 2003’s average speeds for portion on the Champs Elysees circuit, but an average of about 50 km/h (31 mph) is not unusual. The final sprint is often north of 65 km/h (40 MPH). If that’s not particularly speedy, I’m curious about how fast you usually ride.
If the OP is interested in the cultural context surrounding the Tour, I can’t recommend the following book highly enough: The Tour de France by Christopher S. Thompson - eBook - University of California Press
This cultural history was written by an actual historian, so the book is refreshingly free of the hagiographic tone typical of sports writing. It’s also a delight to read…it’s no dry academic treatise.
I was particularly interested in how early 20th-century political factions tried to appropriate the race to advance opposing dogmas. IIRC, the communists liked the Tour because riders in a breakaway (and in the peloton in general) share the work at the front for the benefit of all. The fascists liked it because the winner, after struggling mightily, demonstrated his superiority and reaped the rewards (or something like that).
The OP asked about dangers involved in watching the Tour in person. In any given Tour, there are always a few spectators who get hit (or nearly hit) by riders because they’re looking through a camera lens and can’t judge how close the peloton is. It’s painful to watch! If you’re going to shoot photos, make sure you’re out of the way.
The crash in this video was caused by a gendarme, not a spectator, but he was looking through a camera when it happened.
[sup]1[/sup] Each lap of the Elysees circuit is about 6 km, so ten laps is about 60 km. At 45 km/h, those ten laps would take about an hour and 20 minutes.