Apparently, luminaries are known as farolitos in New Mexico, but their beginning is older than an American state, and the fires sometimes appear as bonfires rather than just candles in a bag with some sand in the bottom. The result is the same: light. Maybe it represents Jesus as the light of the world, but it was also apparently done to guide the spirit of the Christ child to homes where the luminaries were burning. Kind of like stockings for St. Nick.
Supposedly, Mary and Joseph followed luminaria in order to find the lodgings in Bethlehem. Then again, it didn't exactly lead them to stellar accommodations if that's the case. Later, people would create bonfires to communicate and show others the right path. French settlers used these fires along the Mississippi to show Pa Pa Noel where to go to drop off gifts. Pueblo Indians lit paths with smaller lights, in a tradition they learned from Mexicans, who had been lighting paths with fire for Christmas since at least the 16th century. I am not sure if the fires lit for Mary and Joseph were small, but many of the fires set on Christmas seem to have been actual bonfires rather than small fires in paper bags, which is more of a recent adaptation to a society that frowns upon untended bonfires along roads.
Based on the age and separate cultures lighting a path with fire on Christmas, I'd say it totally originated in Europe, though putting the fire into little paper bags might be an American twist on the tradition. However, I don't know if the Spanish settlers in Florida are responsible for the use of luminaries here. There are a lot of articles about tourist attractions and churches trying to get people to show up to see Christmas luminaries in Florida, but I don't see mention of whether the tradition in Florida predates the one in New Mexico. Based on other evidence, you can assume luminaries or similar bonfires were used to some degree in Spanish settlements in the area, so we can go ahead and pretend Floridians have been using them since the time when the Spanish were killing the French Protestants in the name of the Catholic church.
While I'm sure Christmas luminaries are plenty old, I did not find any examples of people lighting the way to church on Christmas in European cities today. I did find a festival of the Luminaria in Spain that is 500 years old. This is not a Christmas tradition, exactly, but it's generally during the Christmas season. Horse riders take their horses through big fires to purify them. Even thought it's not a Christmas Eve thing, it's pretty striking when you look at the photos.