It’s great to hear that you are planning on cycling from London to Paris soon. When will you be doing the ride? Independently or part of a group?
As for training as part of your commute. It’s so difficult to find the time in a busy week to go out and cycle for a couple of hours a day, doing this on your commute is one of the best ways to do this.
Your daily commuting will give you a good level of general fitness, but you do need to get a number of longer rides under your belt to train for endurance. The weekend rides are great for this and it’s good to follow a training plan like that found on this site.
Your body needs to get used to burning energy over a long period of cycling and doing so on consecutive days, just like the London to Paris bike ride. Therefore make sure you do quite a few long rides in the weeks before your trip.
I would say if you can comfortably complete a 60 mile ride like the London to Brighton then you will be more than prepared for Paris.