  We study the matching of Froggatt-Nielsen theories of flavour onto the
Standard Model Effective Field Theory (SMEFT), upon integrating out a heavy
Beyond-the-Standard-Model (BSM) scalar `flavon' whose vacuum expectation value
breaks an Abelian flavour symmetry at energies $\Lambda_\text{FN}$ well above
the electroweak scale, $\Lambda_\text{FN} > \Lambda_\text{SM}$. We include
matching contributions to the infrared $d_\text{SM}=6$ (Warsaw basis) SMEFT
sourced from ultraviolet contact terms suppressed up to order $1 /
\Lambda_\text{UV}^2$ in the Froggatt-Nielsen Lagrangian, where
$\Lambda_\text{UV} > \Lambda_\text{FN}$ is an arbitrary deep-ultraviolet scale
where further unspecified BSM particles are dynamical. This includes tree-level
(one-loop) ultraviolet diagrams with $d_{\text{FN}}=6$ $(5)$ effective
vertices. We first do so with a toy model, but then generalize our findings to
arbitrary Frogatt-Nielsen charges. Our results indicate a rich and non-trivial
signature of Froggatt-Nielsen theories on the (otherwise) model-independent
operators of the SMEFT, and we briefly speculate on extending our analysis to
broader classes of BSM flavour models, e.g. non-Abelian and/or gauged theories.
We thus take an important step towards determining how to use rapidly
developing theoretical and experimental SMEFT technologies to gain unambiguous
insight into the SM's longstanding fermion flavour puzzle.
