Its pretty obvious that Fantastic Four will be set in the present just like the original series and the other superhero franchises out there.
"This is our chance to make a difference" - Sue Storm - The Invisible Woman
"He's stronger than any of us but he's not stronger than all of us" - Reed Richards - Mr. Fantastic
"We could these powers to help people" - Johnny Storm - The Human Torch
"You can't fix this, nobody can" - Ben Grimm - The Thing