so don't get hung up on what you call them

There's no need to tell them something that is incorrect. Instead of calling them cognates you can tell them the origin of both suffixes in their respective languages and say how it's interesting that two languages choose roughly similar ways to express something morphologically. Calling -ly and -mente cognates is doing them a disservice which very well may come back to haunt them later on in life. Like telling them that pi is three exactly, instead of around three,

Ceci n'est pas un seing.