Some Victorian name book writer derived these names from the Old German Adelheidis, and all the modern baby name books repeat this. It's not impossible -- after all, Louis began as Chlodwig -- but it becomes unlikely when one can find other sources.
Now you must remember that most Victorian name book writers attempted to derive absolutely all European names from Hebrew, Greek, Latin, or Old German. If they could have stuck to just the three "holy languages" they would have been happier, but there were just too many Germanic names in use to ignore. One never, ever sees a name tracked back to equally ancient but non-scholarly languages like Etruscan, Gaulish, Phoenician/Punic, or Ancient Egyptian. The modern writers of baby name books normally know even less of languages, and merely compile old information. They certainly aren't going to rock the boat. Even so, there is plenty of good evidence that names survived from the scholastically- ignored people. The first to strike me during my researches for People's Names was Alicia.
Alicia is often listed as a romanticised version of good old dependable English Alice. I believe this is putting the cart before the horse, as was often the case with Victorian namsers. Alice has suffered, like many Continental names, being chopped down to suit the abrupt Anglo-Saxon ear. Alicia or Allicia is the older form as I found it in medieval references.
An onomasticon is the set of words or sounds which are acceptable as names in any culture. Some onomasticons share a lot of names; some names have to be changed in pronunciation to be acceptable to certain onomasticons. In the ancient Gaulish onomasticon, there is attested by inscription the male name, Allicio, whose feminine form would be Allicia. This puts Allicia in France before the Germanic invasions.
Now, the Germanic invasions did not annihilate or replace the bulk of the Latin-Gaulish population of France. Their numbers were nowhere near large enough for the job. Instead, they became the military overlords of the Gaulish population.
As belonging to a ruling class, the Germanic onomasticon was higher in status than that of the Romanised Gauls. So Allicio and Allicia were used by commoners thereafter, and disappear from the history books as all the rulers, generals, and other worthies have Germanic names or Latinised Germanic names.
Allicia reappears as a name, not in England or Germany, but in France, where one would expect a Gaulish name to survive. In the Middle Ages, they often used the diminutive form Allisoun or Allison.
It is not the only Gaulish survivor. Many of the others, peculiarly French names, like Etienne, have been forcibly attached to utterly unrelated Greek or Latin saints. In this case, Stephanos has only a T near the front and an N near the end in common with Etienne, yet the -ienn- structure is common in the Gaulish onomasticon, if you will look at that chapter. In the same way, Andres, though close, need not derive from Andros when there is an attested Gaulish "Anderes" from BCE. However, all these Gaulish names would have a pagan odour, and were probably attached artificially to sacred sources so that they would be acceptable in the sacristy.
Note that as I live in the middle of the Pacific, I do not have access to the early (300-1300) French church registers where the evidence for or against this theory lie. I can only hope that one of you stopping by here may take up the work. Looking outside the few languages considered by Victorian scholars for the actual roots of names, and tracing their history of modification in use, is a job for many hundreds of researchers, which needs to be done. The onomasticon of a people can tell historians a great deal about them. At present, there is still too much complacent acceptance of the dominance of few languages and their cultures, burying the actual contributions of others to what we are today.