After Britannia shut down its unsuccessful German long-haul branch operating two B767-300ER, the German holiday market (it is technically not a charter market, because the flights are scheduled ones and it is possible to individually book seats on them), has concentrated on LTU and Thomas Cook Airlines (unfortunately no barfing Smiley in the library, so just imagine one here instead) to provide long-haul capacity.
On some markets, there may be airlines from the destination countries also providing some capacity, e.g. Air Transat to Canada, but since the German public seems to to be reluctant to fly "unknown foreign" airlines, the market appeal of those competitors seems to be fairly limited.
Some tour operators also offer flights on "regular" airlines as part of an IT package. I remember that some use(d) Air France for flights to the popular Domincan Republic destination SDQ (connecting in CDG, so don't get exited about nonstop AF longhauls from Germany).
Homer: Facts are meaningless. You could use facts to prove anything that's even remotely true!