Put it simply, the information of the info box is basically correct.
This relationship was forged as a kind of by-product of family politics of the Luxemburgs, the new dynasty of Bohemia in the 14th century.
Luxemburg dynasty who took over Bohemia from the Přemyslid dynasty (The last male hair had died in 1306) by political marriage originally came from the border region between France and HRE. They were generally in good terms with the two French dynasties, Capetians and Valois as well.
Do you know that the birth name of Emperor Charles IV of HRE (King Karel IV of Czech-Bohemia) was not in fact Charles? He had been born as Wenzel (Václav in Czech), traditional name for the former Přemyslid dynasty, in 1316. When young 'Wenzel' was only 7 years old, King John the Blind of Bohemia sent him to Paris, and he would have stayed there in further 7 years (until 1330). Then, King Charles IV of France (d. 1328) gave his name, 'Charles' to Wenzel, future Emperor Charles IV of Bohemia. Elder King Charles of France was in fact an uncle for Wenzel- young Charles: The former's wife, Maria of the Luxemburgs, was a sister of King John of Bohemia. On the other hand, future emperor's first wife, Blanca Margarete, also came from the Valois, a new royal family of France. They got married in 1329 under the auspice of the groom's father, John.
It was rather John than young Charles (now) of the Luxemburgs that cling to this political alliance between the Luxemburgs and the French dynasties. Just after a few weeks after Charles's election to the king of Germany in 1346, both John and now king-elected Charles took part in the famous battle of Crecy on the French side, and John met his end in this battle field. Some chroniclers of the Hundred Years' War, such as Froissart, actually record this death of old John who fought for his old political allies.
I suppose that King Charles of Bohemia-Germany turned his eyes mainly from the West (France) to the East (past of the Empires) after the deaths of his father in 1346 as well as his first wife in 1348, as best represented by his choice of new wives (he got married four times in his lifes), however: The 2nd came from the house of Pfalz, 3rd was of Schweidnitz, and his last wife was of Pomerania in NE Germany (Kintzinger 2003: 410).
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