Don't know if I can add anything others haven't said before, but in my honest opinion you really don't want to drive from Paris to Rome. That's 1400 kilometers (same as between Dallas and Denver) and, if you want to stop somewhere en route, the drive will take two whole days of your vacation. Plus August is the holiday season in Europe and the roads are jammed. A flight between the cities is much more considerable.
I could vouch for some of the alternatives others have suggested, and Paris - Nice (French Riviera) sounds very nice. That would offer greater variability to the vacation. A train between Paris and London (abt 2 hours from center to center) is also good, but then you would limit yourselves to two world class cities only. Rome is great and unique, but it's a long way from Paris. And eight days in either Paris or Rome only with possibly a couple of days trips somewhere in the surrounding area would be comfy too.
Have a good trip with your family - and be prepared to walk many, many miles
