You need to understand that since every note played on the piano starts to fade away as soon as it is played, almost everything in piano music is actually an "audible illusion". What you "hear" is not what the sound that you would measure with a scientific instrument!
What Satie means is that the tune ends with a long F (the tied notes) but at the same time the chords in the accompaniment also include F's.
The attached picture shows "how to play it", but unlike the original it doesn't show what it means musically.
Using the sustain pedal as shown means there is no audible gap between each successive F. If you graduate the dynamics correctly, the listener will "hear" the tune ending in single long F, as Satie wrote it.