The verb form 'sieht' is 3rd person singular, so in this case it must be 'she sees him'.
If it was 'Sie sehen ihn' it could be either 'They see him' or 'You (formal) see him' (Sie=You formal has capital 'S', sie=they has small 's'). If it is capitalised because it's at the start of the sentence you just have to work out which one it is based on the context.
"She is seeing him" sounds as if it means something like "she is visiting him" or "she is going out with him" or "she is catching up with him" or something like that. This means literally she sees him, as in she perceives him with her eyes, and you generally wouldn't say that as "she is seeing him".