No, it doesn't. You could make one by adding "ly", but "widespreadly" would sound weird and people would probably tell you it's incorrect. Also, I have never encountered a situation where I needed to say "widespreadly". I think you will be able to manage fine with "widely". You could say "widely spread".

Having read Dan Smith’s comment on my first answer (Thanks Dan), I wonder why I wrote “You could say ‘widely spread’”, it makes no sense that I did so. You can say it, but it would be used as an adjective, not an adverb (I can't imagine it would, at least), so it wouldn’t be an alternative to the non-existing word “widespreadly”. But no need to despair, just use “widely”, as Su.Ki. wrote.