Kevin Feige was on The Official Marvel Podcast. In today's episode, a little before the 6-minute mark, he confirmed that the poster artwork for The Fantastic Four was influenced by the 1960s because the film is set in that time period.
He also made a shoutout to all the "smart people" who saw the cityscape in that "Happy 4-4 Day!" artwork (with Human Torch flying) was different to that of the usual New York, possibly hinting that the movie takes place elsewhere at the very least or in another universe at most.