In the first movie, no significance is apparent.
Nothing about a future Dark Lord being born is mentioned anywhere in the movie, and none of the events have any particularly clear parallels to anything significant that happened in his life. Credence is an orphan, as was young Tom Riddle, and Grindelwald was rising to power, as Lord Voldemort would later do, but nothing that happened is clearly related to him.
However, there are going to be 4 more movies so it may be shown to have significance later.
Later in the series, though, it may be revealed that the year did have some kind of significance, although none is apparent now. It may be a purposeful detail that we discover later in the series. However, it may also mean nothing, or the date in itself is simply a reference to the Harry Potter series, and has no further significance past that.
It seems likely that choosing 1926 means something, even if it's just a little Easter Egg.
The choice of Lord Voldemort's birth year may have been simply a nod to it, even if it doesn't tie together into a bigger story, like how Newt Scamander appeared on the Marauders' Map in the movie of Harry Potter and the Prisoner of Azkaban.