We want to travel from London Heathrow to Normandy in March and stay 2-3 days before returning to London. What is the best way to get there and do you have any suggestions on what tours are the best to take?
If you are not driving and wanting to go there in one day, you would either fly Heathrow To Paris and then take a train from Paris Saint Lazare Train Station to Bayeux or Caen, or go from Heathrow to London St Pancras train station and take the Eurostar train service London to Paris Gare du Nord and then a taxi to Saint Lazare Train Station.
I did my own tour but If you are interested in the World War 2 D-Day stuff this tour company is highly recommended if you decide on Bayeux or Caen as bases:
https://www.overlordtour.com/
Just be sure to take warm clothes.
We used this method at the end of March in 2013 because we were staying in London: "London St Pancras train station and take the Eurostar train service London to Paris Gare du Nord and then a taxi to Saint Lazare Train Station." We trained to Bayeux, stayed five nights. Did two days of D-Day touring with Dale Booth, divided a day between the Tapestry and walking around Bayeux, and rented a car to see Honfleur.
Since you're already at Heathrow it might be more convenient to fly.