The map shows the Mexican Cession, this is, the U.S. purchase of territories from Mexico to the West as agreed in the Treaty of Guadalupe-Hidalgo, in 1848, the year after the end of the Mexican-American War of 1846 -1847. An additional territory called La Mesilla (south of Arizona and New Mexico) was purchased in 1853.
the Franks were a West Germanic people or tribal grouping. The Vikings, on the other hand, were not so much a tribe but a North Germanic occupation of plundering, looting and trading.