Higgs Self-Coupling at the Future Circular <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml

Single Higgs production at FCC-ee probes the Higgs self-coupling at next-to-leading order (NLO). Extracting a bound requires a global analysis accounting for other possible new physics contributions up to NLO. We determine the FCC-ee sensitivity to Higgs self-coupling modifications δκ_{λ} within the standard model effective field theory framework, including for the first time flavor, LEP, LHC, and FCC-ee observables in a global analysis with all leading NLO effects via one-loop renormalization group evolution, as well as incorporating finite NLO contributions to electroweak precision and ZH observables. The global sensitivity to δκ_{λ} is estimated by marginalizing over the effects of all other operators, bringing flavor considerations to the fore. We find that, under reasonable assumptions, FCC-ee sensitivity to δκ_{λ} can exceed that of the HL-LHC.