I also had issues with F Major.. but then I started to play this other F Major derivative. I -think- it's an Fadd7 which is probably an F7 or a FMaj7.. I am too tired right now to do the math and work out which particular chord it is.
||-----|-----|-----|-----|
||--1--|-----|-----|-----|
||-----|--2--|-----|-----|
||-----|-----|--3--|-----|
||-----|-----|-----|-----|
||--T--|-----|-----|-----|
Anyway.. the numbers indicate which finger to use.. the T represents your thumb. To play the F on the bottom E with your thumb like this, you will need to curl your thumb over the top of the fret board. This is how I used to play ALL my F Major chords.. Whenever I'd see an F Major in the sheet music or whatever.. I would play that chord.. It's also extremely easy to switch from this chord to any of the other open chords, or from any open chord to this chord.
Benoit is definitely more correct than I am in what he is teaching you there.. but I thought I would offer an alternative..
These days I use a barred chord for my F Majors..