For the verb meaning, primarily, to dismay or shock, appal is the standard spelling outside North America. Appall is standard in the U.S. and Canada. This has been the case since the late 1800s, though the old double-l variant—which was the prevalent form everywhere until around 1800—had long been gaining ground. Appal continued to appear often through much of the 20th century but has almost completely disappeared over the last few decades. Outside North America, meanwhile, the spelling with one l continues to prevail by a large margin.
Of course, even where the single-l spelling is preferred, the l is doubled in inflections such as appalled and appalling. Appals, however, has the single l.