Going for a run in Paris

Trocadero - Eiffel Tower - Champ de Mars - Ave de la Motte Picquet - Invalides - Pont Alexandre III - Grand (&Petit) Palais - (lower) Champs Elysees - Place de la Concorde - Tuileries - Pyramid du Louvre.
This is about 6km (or 3.5 miles)

Just follow the Seine! Cross a bridge at your halfway point and come back down the other side...nothing more lovely!
A run that goes from the Eiffel Tower running east all the way to Parc de Bercy, crossing the bridge there, and then coming back is a great route - about 5 miles or so round trip. You could shorten it up by turning around at Isle St Louis crossing the bridge behind Notre Dame onto the Isle de la Cite, and taking the Pont Neuf to the other side and continuing from there. You could even jog down the steps occasionally and run along the low path that runs along several parts of the river. Beautiful!
Running along the Seine early in the morning or on weekends will avoid most of the traffic. I really couldn't speak to etiquette...not sure of anything specific that would be specific to Paris!

Watch the cobblestones on the lower Seine and Place de la Concorde.

Go early before the pollution builds up.

A lot of people run in Parc Monceau, it has a sort of track around the perimeter and going early there will be lots of runners who more or less crowd out the strollers and aimless wanderers.

Luxembourg Gardens. My favorite park in Paris. Lots of runners on the running path along the fence all around the park (inside). You won't have to worry about cars or cobblestones.

Luxembourg Gardens. Beautiful place to run. Also if you can make it out to Bois du Boulogne that would be beautiful too and lots of space.

I like certain parts of the Bois de Boulogne but many areas can be sketchy. I wouldn't feel safe running in many areas there alone.

The run along the Seine to the Tulieries (excuse the spelling) and the Louvre is a nice run in the morning. I enjoyed the relative tranquility around the Louvre. No tourists, just a few runners in the large plaza near the museum.

Thank you all for your suggestions and tips - much appreciated!

I would think the best jogging route would depend on where you're starting from.