Traveling a more or less linear, north to south direction seems to make the most of your time and avoids much backtracking, so arriving in Paris and departing from Rome sounds reasonable. In April/May, it won't yet be scorchingly hot as you move south, but if you were visiting in July or August, you might consider starting south and moving north to keep somewhat cooler temperatures.
For car rental, since having a car in a big city is generally a traffic and parking hassle, perhaps you wouldn't need the car right away. . . maybe wait at least until you're leaving Paris? With more than 3 weeks of holiday, rather than "renting," you may want to look into "leasing" (also referred to as a long-term or month-long rental) -- see what Auto Europe offers online. To fit through narrow streets and in tight parking spots, we've always gone with the smallest car we can get - but it's usually been just 2 or 3 of us. With 2 kids and child seats, plus luggage, you may need a bit larger vehicle. Also, is hubby bringing his own bike, or shipping it to Europe, or renting a bike or bikes over there? You may need additional stowage space and/or a bike rack!
We once rented a car in Portugal and turned it in in Spain, incurring a hefty additional fee for returning it in a different country, but it saved us time and inconvenience. Generally, you can turn in a car within the same country (even if it's a different city) without an extra fee. Also, make sure that your rental contract allows taking the car to a different country, and that the country/countries where you're heading are not on a prohibited list with that company. Check with each rental company you're considering to confirm their policies.
Another option would be to rent a car in the first country and turn it in before you get to the next country, then cross the border by train or bus, then pick up another car in country #2 and turn it in before getting to country #3, then pick up a third car. If you're not completely accustomed to driving on the right, starting off in a less-trafficked location might help ease you into driving than would a place with heavy traffic. Also remember to go anti-clockwise at roundabouts! Before leaving home, get an International Driver's Permit for each driver, necessary in both Italy and Spain if the police want to see it along with your home driver's license.
Six years ago, we were able to park in the lot just steps away from the entrance for Mont Saint-Michel, but I understand now that you park on the mainland and take a shuttle to the base of the Mont. Maybe that's another reason you might not necessarily need a car right away in Normandy, if you find another way to get there?
Last, a Foodie tip: in November last year, we visited San Sebastian, Spain (with expensive underground parking garages, another thing to consider when you have a hired car) and had lunch at nearby restaurant Martin Berasategui (http://www.martinberasategui.com/en/inicio). Lunch was not quite as expensive as dinner would've been, but with course after course, it was our day's entertainment and we weren't hungry for the rest of the day! When we made our reservation, they asked about any dietary preferences or restrictions. I'm sure the talented chef and his staff would use all 3 Michelin Stars to accommodate your vegetarian needs (and can also produce fabulous seafood, if you like).
