You're not going to like this......

in a straight line Hahn airport is actually slightly closer to Luxembourg than Frankfurt, there is a fairly regular bus service but it takes 1hr 45 mins and costs €12 euro each way (which is often more than the Ryanair flight price!). The bus details are here http://www.bohr-omnibusse.de/routes/wtc/routes.php?action=detail&route_id=2&language=en - note that you basically have to be at the bus stop in Frankfurt at least 4 hours before your flight departure.

Unfortunately Ryanair use the name Frankfurt in the Airport name erroneously as the airport is 124km from the centre of Frankfurt, the bus will take you to the main railway station in the middle of Frankfurt, it can take up to 2hrs for the bus journey (maybe more at busy times) I'm not sure if it's the same bus but there is also a service to the main Frankfurt Airport from Hahn.