Your best bet is to start with a good guide book, such as the Michelin Green Guides. The books have recommended itineraries and a whole of useful information on sights and places to stay.
I would spend 3 days/nights in Paris
Then go to Amiens by train - takes about 1 hour or so.
Amiens is a good base for Vimy, hire a car there and do your Vimy visit and also drive around the area and visit other WW1 sites on the Somme - you will find them everywhere!
Amiens I thought, was a lovely city with a good 'vibe' and a very walkable centre, there is plenty to see/do there and lots of nice bars/cafes/restaurants in various squares and at the riverside on the Quais.
Arras would be an alternative place to stay and is nearer to Vimy than Amiens. However, whilst it is a lovely town, it does not have quite so much to do 'in town' as Amiens does.
That is very helpful advice, thank you!