1. Go on a Wednesday
The Wallace Collection opens at 10h00. You obviously want to be there as soon as it opens. Once in, go to the first floor and aim for West Gallery III.:
Assuming it takes you one hour to get to the painting and admire it in its full glory, you should be out of there and into a taxi by 11h00.
You'll then be on a taxi for 16-17 minutes towards St Pancras.
Once there you could either get the the 12h24 train to Gare du Nord.
This leaves you enough time to check-in, go through passport controls and drink an extra-hot skinny hazelnut frappuccino whilst waiting for the train.