Both are correct but it depends on the context.
This is a very fine thread." means the thread is not wide.
"This is a very fine day" means it is a nice day ( the weather is good) but it sounds old-fashioned to me.
"I speak English very well"
"I don't feel very well" meaning I am sick"
very well can mean "yes, okey" in some places.
a: Why doesn't anybody ever clean the oven?
b: Very well, I'll do it