The FPS in the F3 screen will not always reach the value set for the maximum FPS under video settings. An example: if the maximum FPS is set to 120, the FPS shown in the F3 screen will only go up to 116, whereas in 1.12.2 it would just go up to 120 just fine. If the maximum FPS is set to 10, it will reach 10 FPS just fine in the F3 screen.
I tested this with both vsync off and on, this does not make any difference.
Here are some more max FPS settings I tested:
Max FPS setting FPS in F3 screen
30 30
40 40
50 49
60 59
70 68
80 78
100 96
120 116
However, once I change the max FPS setting and I click back to game, the FPS in the F3 screen actually goes up to the max FPS value for just a second or two.
I already reported this bug earlier (MC-130881) but it got resolved for an invalid reason in my opinion. It got resolved because the mod thought that the bug was about the difference between 60 and 59,997 fps. It is not, because the bug occurs on other max FPS values too.
I can't confirm this behavior because the fps meter in the F3 screen can be misleading (it doesn't update quickly enough), and the debug screen itself can cause significant frame drops that prevent you from reaching your max.
However, using ALT+F3 we can look at frametimes, which I've attached to the issue. As clearly seen, 1.12 has more erratic frame times, with ones that go well above and below 60. In 1.13, it is much smoother but F3 might report 59. It almost looks like the FPS issue was in the previous version and fixed in this one and is intended behavior.
EDIT: I posted the two versions set to 120fps and 30fps. 1.12 continues to have erratic and inconsistent frame times compared to the smoother 1.13. Because of this, 1.12 actually doesn't run near the target framerate if you look at each frame time since it's so inconsistent.