Obviously practicing is the best thing to do, but here are some tips that might help you.
I recommend going through a list of F2L algorithms and comparing them to your intuitive "algs". You should make sure that you are not wasting any moves on any of the pairs.
I think a mix between intuitive F2L and alg-based F2L is best. By that I mean you should definitely be able to see how all of the pairs work, but you should also be able to solve each pair without looking. I know a few people who use intuitive F2L and they get into the bad habit of following the pair with every turn, and what ends up happening is they see the pair, break it up/pair them up, then look at the pair again to see how to insert it. This is very bad, and it slows you down A LOT. You should be able to look at the pair and be able to break it up/pair it up and solve it in one fluid motion while at the same time knowing what you are doing. This is what I mean by a mix between intuitive F2L and alg-based F2L.
This will also help you look ahead. If you can solve every F2L pair without having to look at what you are doing, you can use this to your advantage to look around the cube for pieces while you are solving a pair. Looking ahead is THE KEY to a good F2L.
You should also keep track of pieces that are "stuck" in the F2L. By this I mean if there is an edge that is in the middle layer or if there is a corner in the first layer. As you see these, keep a mental note of what pieces they are and where they are. Don't solve the pair until you see where the other piece is. That way once you see where the other piece is, you automatically know what the pair is.
Also, keep track of the slots that you have used and the slots that are still open. You can use empty slots to your advantage to avoid cube rotations.
It also helps to know a few tricks. One of my favorite F2L cases is this: U R' F R F' R' U' R (do the inverse to set up).
These are just some of the things that have helped my F2L get pretty solid. Hope this helps!