We will be spending a few days in London first and then 2 weeks in France. The first 3-4 days in France we want to see some of the Canadian war memorials. Should we cross the channel and begin touring from Calais & Dunkirk down to Vimy, Ypres, Somme and then down to Paris or rather fly into Paris and rent a car and head north from there?
Well, coming from London I'd certainly not fly to France. I'd probably take the train, but...depends on other trip details.
Have you been to France before? Where else in France will you be going on this trip?
Sounds like Paris is part of this trip. The one thing I would look to avoid would be driving in Paris itself. Maybe take the Eurostar from London to Paris, spend some days there in Paris, then when you are ready to depart from Paris, pick up a rental car at a location outside the center but accessible from public transit, then head for your WWII destinations and onward. Return the car when you are done with the rural parts of France (move on by train or fly home from there).
This is not WWI, but as long as you're in the area you might be interested in a trip to the WWII site, Dieppe where many Canadians gave their lives or were used as canon fodder, depending upon your viewpoint, exploring the possibilities of an Allied landing. The monuments there are moving.
We did something similar a few years ago, but spent more time, and included some of the WW II sites and memorials too. These are all within a relatively small, drivable area of northern France. The Verdun battle sites are quite a bit further east, and might be too far away for your short time window.
The Canadian Veterans Affairs website has quite a bit of information on the WW I and WW II memorials and War Cemeteries in both France and Belgium. The Belgian sites like Ypres and Passchendaele are close enough to be reachable on your visit. Here's a link to their website: http://www.veterans.gc.ca/eng/remembrance/history/first-world-war/road-to-vimy-ridge/vimy8
Personally, I would skip Calais. They are having some serious safety issues stemming from the influx of immigrants to the area. I'd take the Eurostar to Paris, train to a town near your first destination, and rent a car there.
There are many to see. You can visit them on your own or take day tours with a guide to get more information. Ones that I can recommend near Ypres are Essex Farm, Tyne Cot, Saint Julien, Menin Gate (see the ceremony) and the In Flanders Fields Museum.
I only had time to see Beaumont-Hamel in the Somme but it is very nice.
You should be able to take the tunnel train to Gare du nord and then catch one of the frequent trains to Arras, less than an hour's ride. This small city is the jumping-off point for visiting Vimy, a fundamental Canadian experience.
This link also contains information for other battles.
Arras has lots of its own history in both world wars. Then a car can take you across the Somme where there are all too many killing fields and military cemeteries.
The Commonwealth War Graves Commission does a stellar job of caring forf the cemeteries of all the British Commonwealth services. https://www.cwgc.org/find
Dieppe is a moving and deeply saddening experience with the promenade along the harbor beach now guarded by small memorials to the Canadian regiments that were decimated there. But except for the annual remembrance service in August, Dieppe is a quiet place.
Some machine gun emplacements are still visible above Puys, one of the neighbouring landing beaches. The museum for the raid in the middle of the walled town is worthwhile. Known to some as the Operation Jubilee museum, it is privately run by a dedicated family.
Best would be indeed starting in Calais, but I am afraid that getting there from London is not so easy as it looks at first sight. Just a few Eurostar trains stop there daily and likely not at times convenient for you. Further the station is some 10km outside Calais, so a train, bus or taxi to the centre is needed for getting to the rental agencies. Avis has one at Calais-Fréthun, but have no idea if it is the place for picking up the car, however for the visit you have to go to the centre of Calais anyway where the agencies are not far away. Have to say having no experience with this, but nevertheless I think this option is worth to notice.
If it proves too troublesome better is taking the Eurostar from London to Lille (needing 1½ hour) and rent a car from there, it is located within an hour driving from Vimy Ridge and Ypres. But you will loose a lot of time making the ride to Calais and Dunkirk from Lille. Also be aware avoiding the main roads leading to the ferry ports there as illegal immigrants can cause trouble and are also notorious for congestion with trucks waiting for the ferries, but ask the rental agency. Know that going from the UK to France means crossing a time zone and so loosing an hour.