Old English certainly had a cognate for the ancient Germanic element frid! It was friþ (later spelled as frith):
https://www.behindthename.com/element/frith31
https://en.wiktionary.org/wiki/Reconstruction:Proto-Germanic/fri%C3%BEuz#Descendants
I see the Old English cognate of Adalfrid is even in the main database of this website already, I hadn't thought to look for that yesterday evening (as I was tired and about to go to bed). Here it is:
Æðelfrið. It looks like the name was rarely used after the
Norman conquest in 1066, so I guess that's why
Alfred as a variant of
Æðelfrið never took off (or eventually became well-known) in England. It might already have existed before then (perhaps rarely), but died off together with
Æðelfrið.
"It is no measure of health to be well-adjusted to a profoundly sick society." ~ Jiddu Krishnamurti (1895-1986)