Stone Age Columbus (The first Americans - included French sailors?) [Horizon]

It's believed people migrated to the Americas across a land bridge linking Asia and Alaska, with the earliest waves arriving during the Ice Age 20,000 years ago. Indeed, studies of Native American DNA support Siberian and East Asian origins. However, some tribes in the Great Lakes region seem to have an additional DNA group dating to Europe 15,000 years ago.
The iconic "Clovis Point" spearhead found across the continent in fact seems to bear similarities to those of the Solutrean people of South-West France 17,000 years ago, rather than to known Asian technology. This program discusses the waves of migrations and investigates how Stone Age people could have reached America by sailing the Atlantic.
I'm not sure the latest research supports this theory but it's quite interesting to consider how they might have done it anyway.