Air France sent a recent mailing with a super offer if (a) you want to fly from London to Paris and (b) you wish to do this on Air France.
Book by 1 March to secure this fare.
I found cheap tickets very close to this fare on several dates including later in the summer. The flights are typically off-peak, not surprising for a fare this cheap. You earn no miles and have to pay £11 to check a bag.
The comparative BA fare is £41 but does not allow baggage to be checked but you will earn a small number of Avios, especially if you book before the reduction in earnings.
So if you are thinking of a weekend in Paris, it might be a good time to book.