King Henry I of France married a Russian princess in the mid-11th century. How would such a marriage have been arranged, given the great distance between their lands? How much would 11th century Franks, Germans, and Anglo-Saxons have known about Russia?

It's pretty easy to think of the medieval world as defined by frightening distances which caused people to stay at home, and this seems to be the supposition that underlies your question. Nothing could be further from the truth, particularly when it comes to the nobility. Long distance travel was, in point of fact, frequent, if not ubiquitous.

There are many good examples of this, many of them having to do with the theft or trade of saint's relics, but off the top of my head, there are two examples that stick out to illustrate the point. First, King Cnut of England made a pilgrimage to Rome in 1027 for his coronation, a distance which would only be approximately 500 miles shorter than the trip from London to Moscow. Second, Jerusalem was a very popular pilgrimage destination throughout the ninth through eleventh centuries, despite Muslim rule. Basically, if you had a reason to do it, long distance travel was not a major thing.

Unfortunately, Western cultural perceptions of Russia around the year 1000 are not something I know anything about. Hopefully what I've given is helpful.

Some further reading:

Geary, Patrick J. Furta Sacra: Thefts of Relics in the Central Middle Ages. 2nd ed. Princeton Paperbacks. Princeton, N.J: Princeton University Press, 1990.
Genicot, Léopold. Rural Communities in the Medieval West. The Johns Hopkins Symposia in Comparative History. Baltimore, Md: Johns Hopkins University Press, 1990.
Gelichi, Sauro, Richard Hodges, and Michael McCormick, eds. “Comparing and Connecting: Comacchio and the Early Medieval Trading Towns.” In From One Sea to Another: Trading Places in the European and Mediterranean Early Middle Ages: Proceedings of the International Conference Comacchio, 27th-29th March 2009, 477–502. Seminari del Centro Interuniversitario per la storie e lʹarcheologia dellʹalto medioevo 3. Turnhout: Brepols Publishers, 2012.
Fossier, Robert. Enfance de l’Europe: Xe-XIIe siècle: aspects économiques et sociaux. 2e éd. Nouvelle Clio 17. Paris: Presses universitaires de France, 1989.
McCormick, Michael. Origins of the European Economy: Communications and Commerce A.D. 300-900. Cambridge, U.K. ; New York: Cambridge University Press, 2001.