You likely can do it on one redemption, it will depend on the routing that you take. Since the redemption is limited to the number of actual miles that can be covered, the route selection will impact your choices.

If you are going in the order that you have listed, I think you will need to fly United out of the US in order to keep the actual miles down and it will lower your charge. You are probably looking at Chicago or NYC. The LON to PAR is a bit more difficult because you cannot fly direct, you will have to go through Frankfurt, Munich, Vienna, Geneva or Zurich on Lufthansa, Austrian or Swiss. This may eat up your actual miles. From Paris to NYC, you can fly United or Swiss to limit the fuel surcharge but the Swiss route may impact your actual mile limit again. Leaving NYC, you can leave out of any of the airports, it doesn't have to be the one that you land in.

I would do a roundtrip from YVR to PAR via LON and see what options come up, looking for a United flight to LON and seeing your options from LON to PAR. Note the flights that you like. Then I would do a roundtrip YVR-PAR-NYC-YVR to see the options available, you may have to change the NYC airport between JFK and EWR to see the different choices. Once I did that, I would call Aeroplan and walk them through the route you are looking at to see if it is doable feeding them the flight numbers.