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Well there are two main problems In terms of melody, it's kind of erratic and all over the place, with a very odd rhythm — so it's going to sound kind of weird regardless. In terms of harmony, the main problem here is that your chord choices don't reflect implied harmonies in the melody itself. Although you are using C, F and G chords from C major, much of the melody would more strongly imply A minor. You want to primarily use "chord tones" in the melody to choose chords. For example, in your first bar, you have the notes A, G, and E with the A note being sustained. This would make Am or Am7 a good choice. The first beat of bar 4 goes "A, C, A" in terms of notes, followed by two consecutive D notes on the second beat. For the first beat, you could stick with F, but you could also use Am. The Dm chord is an obvious choice for beat two, but G would also be a good choice especially if you used F for beat one. However, we then run into the problem that in bar 5, the D note is sustained with a resolution back up to E. In this bar, one would typically expect a resolution back to the tonic. You could still use Am in bar 5 — it's definitely a better choice than G — but it will still not sound as complete. The short answer: Try harmonizing this with chords from A minor and matching chords to shared notes from the melody. If a bar has mostly A,C and E in it, than Am is probably the best choice. Also, never forget that for this reason, every melody implies a chord progression itself. Therefore, strong harmonic flow and voice leading is pretty much inseparable from strong melodic movement