There are a ton of words that end in -cense or -cence. Like, this is definitely a two-parter. And we’re not even getting into words like luminescence or iridescence since those are related to essence and a whole other post on their own.
License is kind of funny. It showed up in the early fifteenth century as a verb that meant to grant authorization to do something. No big surprises there. But it comes from a noun that’s spelled licence, with two C’s (which, frankly, just accentuates how stupid and redundant C is). Apparently there were tons of spellings for the word in Middle English, including lisence, lissens, and licance, which exemplifies why we had to start formalizing spellings. Anyway, licence is spelled that way because it comes from the Old French licence, liberty, freedom, or permission, which in turn comes from the classical Latin licentia, which means the same thing, in other words, a license. The verb form of it, licere (to allow) can be traced back to the Proto Indo European leik-, to offer or bargain. Which…makes sense, I guess.
Innocence showed up in the mid fourteenth century meaning specifically the “freedom from guilt or moral wrong”. It comes from the Old French inocence, innocence, and classical Latin innocentia/innocens, which are just innocence and innocent. When you break up the word and look at its roots, it gets seven better. The in- means not in this case, while the centia/cens part of the word comes from nocere, hurt. That fits since innocence is non-harming, right? Well, nocere comes from the Proto Indo European nek-, which means…death. It’s where necro- comes from!
Incense first showed up in the late thirteenth century meaning something that gave off a sweet scent when burned. It comes from the Old French encens, from the Late Latin incensum, that which is burnt. That in turn is from the classical Latin incendere, to burn, which might sound an awful lot like incendiary to you. And it should, since that word is from the same place. This time the prefix in- means in while the rest is from candere, shine, glow, or be on fire. And of course that’s where candle comes from. It can also be traced all the way back to the Proto Indo European kand-, glow or shoot out light. So light = fire = stuff burning.
TL;DR: None of these words are related. Like, at all.