A first person mode has been a much requested feature for Fortnite for a very long time, and there have been indications that it is in fact coming. And now it seems like the wait is allmost over. According to several dataminers, it has now been revealed that the first person mode is coming next season (Chapter 4 Season 2).
If this will be combined with a no-build mode to make it more of a regular shooter remains to be seen, but that has also been a thing that the Fortnite community has been asking for. Adding this would potentially make the game more attractive for a new audience as well, so we could imagine it's something Epic Games is considering.
It's worth pointing out that while even though multiple sources points towards the same thing and the information comes from datamining of the game itself from proven leakers - it's still no official confirmation.