Unfortunately, the June 6 timeframe coincides with peak season in Europe. Nonetheless, there ought to be less pricey flights available.
A Google search for D-Day tours will turn-up plenty of leads for guided experiences, many from England.
Based on my own experience, you and your 11 year-old will find no shortage of interesting and compelling people, places and stories, even without a tour. Just walking toward the bluff at the American Cemetary at Colville-sur-Mer and overlooking Omaha beach gives you a better understanding of the day's magnitude than any account can convey. Pointe du Hoc, Sainte Mere Eglise, Bayeux (catch the tapestry as long as you're in town), Caen, other beaches, and other cemetaries offer their own bits of the story. Plan on several days to explore and soak in all the region has to offer.
While there are many credible texts on D-Day, John Keegan's
Six Armies in Normandy is a complete account, representing all sides, that won't intimidate an budding historian of 11 years.
If I can help at all, shoot me a direct e-mail at
pentoad@aol.com.