Both names reflect the presence of hot springs, which since Roman times have been channeled into baths. Aa- is an Old German cognate with Latin aqua, both meaning "water". In French speaking areas the old Roman spa-towns often softened their names to "Aix", hence Aix-en-Provence is an old Roman spa-town in Provence?. Aix-la-Chapelle was called such because of the great chapel at Charlemagne's palace, where he spent most winters between 800 and his death in 814 in order to enjoy the hot springs.
[Robert Browning's]? poem "How they brought the good news from Ghent to Aix" refers to Aachen.