I live just outside Kaiserslautern, so quite a bit South of where you’re going, but you could quite easily get into the Pfalzerwald with not too much pain. I’ve not personally ridden in the Eiffel, but there is a bike park there and probably countless other riding options. A good place to have a look would be on MTBR, as there are a lot of US military based around the S of the Eiffel and the Hunnsruck hills. I’ve heard a trail mentioned around Manderscheid Castle numerous times. There is also Stromberg flow trail not too far south of where you are if you want a bit of DH.
If you do get into the Pfalzerwald, maybe check out the Felsenwanderweg at Rodalben. 48km of waymarked singletrack, not strictly for bikers (And probably best on a week day), but it rides like purpose built stuff imo, no huge climbs, just nicely flowing singletrack with some nice rockery. Stays fairly dry too as it’s all sandstone.