Here's my two cents worth...

Good melodies will nearly always have a tug-o'-war happening between consonance and dissonance with the harmony. This is how music works.

Often the non-harmonic tones -- such as the F you mention against a C chord -- are on non-accented notes. By this I mean, for example, in 4/4, the main accents are beats 1, 2, 3, 4 and the strength of these accents are strong, weak, medium strong, weak. So if one wants to use a non-harmonic tone for a melody that has 4 notes in a bar, beats 2 and 4 are good places to put it.

What happens when there are eight notes in a 4/4 time signature?

It's turns out that the "strong, weak, medium strong, weak (simplified to SWMW)" works for most groups of four evenly spaced notes.

For example, with eight notes in 4/4, there are two melodic groups of SWMW -- one for the notes on beats 1 and 2 of the bar and then and a second group of SWMW for the notes on beats 3 and 4 of the bar. When fitting lyrics to music, which I have been doing a great deal over recent years, it's very important to be aware of these melodic sub-groups and the musical strengths of the various notes within them so that lyrics sit comfortably.

Again... in this example the weak beats are a good places to locate the non-harmonic tones.

That said, it's always possible to put non-harmonic tones on strong beats. To do this, they nearly always resolve down by either a tone or semitone to the closest chord tone. Mozart delighted in such melodic notes. They are called appogiaturas or accented non-harmonic tones.

I don't know if these thoughts will help, but they might give you some ideas as to where you can being looking for answers.

Regards,
Noel

MY SONGS...
Audiophile BIAB 2024