I have taken many RS tours but this will be my first My Way tour. Is there anything I should or could buy ahead of arriving in France that would expedite entry into some of the sites to visit during this tour?
It is going to depend on what you want to see and do. If you want to go up the Eiffel Tower, have timed entry status at museums, Versailles , St Chapelle or simply the convenience of prepaid tickets for a sightseeing boat, look at buying tickets in advance.
Don’t worry about Notre Dame tickets. The walk up line goes quite quickly.
I would start by checking out the websites of the specific places you may want to visit and put together a spreadsheet of when tickets go on sale for different sites in Paris. Not everything requires an advance ticket, but the biggies do-Eiffel Tower, Louvre, Saint Chapelle, Musee d'Orsay, L'Orangerie, etc.
Perhaps others who may have taken this specific tour can address the other city destinations and what may require advance reservations, if any.
Hope you have a wonderful tour!