Watch the Try Sometimes online guitar lesson by Jeff McErlain from Essentials: Chord Tone Soloing
Now that you've messed around using the major pentatonic and feel comfortable with that as a scale over the chord progression, start to think about playing chord tones on each chord while on that chord. Always look for common tones between the two chords, C and F in this case, with the C note in common between both.
It's fairly obvious the song is in the key C, so the next thing you want to look for are the notes that are in the scale and in the chords. For example, the F major chord has the note A in it. A is not a great choice over the C chord, but works beautifully on the F chord. Why? Because it's in the chord! I know that sounds silly, but I didn't think about that for many years. Kind of embarrassing, actually.
So, a simple way to practice this concept is to choose one note from each chord and concentrate on hitting that note on the change. Be very conscious in this effort and don't worry about it sounding musical or not. We're trying to introduce a new concept. It's important when practicing to realize that this may not sound all that musical at first. That's fine. Continue to do this with the other chord tones contained in the pentatonic scale.