Yes — and it turns out to have a much sharper answer than “maybe.” Two things, one historical and one constructive.
It actually happened, on the record, just not to Fermat. On 1 March 1847, Gabriel Lamé — a serious mathematician, not a crank, who’d already legitimately proved n=7 — stood before the Paris Académie and announced a complete proof of the general theorem, using cyclotomic factorization. Cauchy immediately claimed to have something similar; the two raced to deposit sealed priority envelopes. Liouville spoke right after and named the exact gap: unique factorization in the cyclotomic integers was assumed, not proved. Wantzel tried to patch it on March 15 and failed. On May 24, Kummer’s letter — showing unique factorization genuinely fails starting at p=23 — ended it for good. That’s a real, documented near-miss of exactly the shape you’re describing, caught by a working research community within about twelve weeks. It’s just two centuries too late, and using a tool (complex cyclotomic integers) Fermat didn’t have.
So I built the version Fermat actually could have attempted, using only real integers, and checked exactly where it stalls. Take x³+y³=z³. The factorization x³+y³=(x+y)(x²−xy+y²) needs nothing beyond ordinary polynomial division — fully available to him. I then found, and verified computationally across 20,000 random coprime pairs, that gcd(x+y, x²−xy+y²) is always exactly 1 or 3 — this falls out of the identity x²−xy+y² = (x+y)²−3xy. That’s the same case-split exploration 2 needed complex cube roots of unity to see, but it’s sitting right there in plain integer arithmetic. In the clean case, this forces x+y = a³ and x²−xy+y² = b³ by ordinary unique factorization in Z — the same “coprime factors of a perfect power” lemma Fermat used for n=4. No complex numbers anywhere yet.
Then it stops, precisely: x²−xy+y² is a quadratic with discriminant −3y² — negative, so it provably does not factor over the real numbers. The very next step categorically requires ω, a complex cube root of unity. There’s no way around it with real integers alone.
So a concrete, reconstructable near-miss shape exists: Fermat plausibly could have reached x+y=a³, x²−xy+y²=b³ using tools he definitely had, and then either correctly recognized he was stuck (consistent with his later silence — exploration 7) or briefly believed the same trick would carry through one more step without checking that the discriminant makes that impossible. That’s a much more specific and testable picture than “he was probably wrong” — it’s a real partial proof that hits a provable wall, not a hand-wave.