For me, there are hints (like endling と) for the word is an onomatopoeia construction, that's the difference... As in, 「ふと気がついたの。」"'Pooh!' - the realization came." Although it's not as childish in Japanese, as they use onomatopoeia words a lot.
I don't think ふと、is not an onomatopoeia construction. In kanji 不図 not planned, not mapped, unexpectedly, etc.
I don't know why they don't write it in kanji though, as both are easy...
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