That theory has lost a lot of legs in the past few years now that DNA results from ancient North Americans have been sequenced and they don't show any affinity to Europeans, such as Anzick-1 who's body was found in a Clovis burial and Kennewick Man who's skull shape was used as proof by Solutrean Hypothesis supporters. https://www.nature.com/articles/nature14625

If the documentary was older than 2015, it's likely they didn't have this information and would be relying on inferences from the DNA of modern populations, which would be complicated by mixed race people.

This is known as the Solutrean hypothesis. I understand it to be controversial, but it seems like everything about this topic is controversial to somebody.

Sounds like part of Thor Heyerdahl's larger theory of vikings everywhere. Part of the story was folks settling the Pacific from South America, recreated in the Kon-Tiki expedition.

Heyerdahl believed that people from South America could have reached Polynesia during pre-Columbian times. His aim in mounting the Kon-Tiki expedition was to show, by using only the materials and technologies available to those people at the time, that there were no technical reasons to prevent them from having done so.

https://en.wikipedia.org/wiki/Kon-Tiki_expedition

Solutrean culture in France predated the vikings by something like 20,000 years, give or take a few. They have nothing to do with each other at all.

It had nothing to do with Heyerdahl.