I read this decades ago and liked it. For a reasonable plot summation I again rely on excerpts from a review by my favorite reviewer - from Analog October 1961:
"…though it is the one I enjoyed most. Basically it is a fantasy… However, there is just enough skeleton of "scientific" rationalization - Holger Carlson may have slipped into an alternate timetrack, the world of mixed chivalry and magic of the French romances of Charlemagne and his knights - for Doubleday to label Three Hearts and Three Lions science fiction. It's $2.95 for 191 pages of grand action fantasy on a highly civilized level, and well worth it.

Holger Carlson is a Danish-born engineer, educated in America, who has gone back to lend a hand when his native land is overrun by the Nazis. In a skirmish on the beach he is shot in the head, and wakes up in a world of witches and dwarfs, fairy lords and elf folk, dragons and giants. A witch tries to trick him; a dwarf and a swan-maiden befriend him; a mysterious Saracen is on his trail; and numerous beautiful women are more than obliging. A student of Carolingian romance may find out who he is before Holger does, but it doesn't really matter. What does is the joyous blend of medieval romance and twentieth century pragmatism that helps Sir Holger handle a fire-breathing dragon and a nereid, warns him away from a giant's treasure…

…we have example after example of what a writer who isn't afraid of wonder can do. Here are "old fashioned" themes and plots, made completely fresh by their handling and completely modern because the author is looking past the play of peril-and-action to the psychological actions and interactions of the characters. Needless to say, a writer who can't make characters come alive can't do this." [P. Schuyler Miller, in a review of 3 books by Anderson]