Ok, so you are using the 4 string variation (probably has a proper name). That's the best F chord to begin with imo.
When holding the B & e strings, you could try making a little barre with the end of your finger. It would be hard to hold the 2 strings with just the tip.
When I do this chord, my index is pulled back (or down depending on how you look at it lol) and I use the area from about first knuckle to the tip to hold the B & e strings. My finger sets at a little angle compared to the strings. Your's may or may not, but either is fine; this ain't geometry class, right?
The good news is, master this and barred B is easy. :)
...so ever since then, I always hang on to the buckle.