My goodness, what an open-ended question.

Have either of you ever been to Paris or Rome before? There's so much to see and you can easily spend weeks in each city. Since your time is limited, you really don't want to be rushing all over the place.

For that reason I would certainly not recommend going to both Paris and Rome; you simply don't have enough time.

I would say that if London is the start and end point, then you should go to Paris and not bother with Rome on this trip. You can spend a few days really enjoying what Paris has to offer and then come back to London at a leisurely pace.