The search for flavons with a mass of Oð1Þ TeV at current and future colliders might probe low-scale flavor models. We are interested in the simplest model that invokes the Froggatt-Nielsen mechanism with an Abelian flavor symmetry, which includes a Higgs doublet and a Froggatt-Nielsen complex singlet. Assuming a CP conserving scalar potential, there are a CP-even H F and a CP-odd A F flavons with lepton flavor violating (LFV) couplings. The former can mix with the standard-model-like Higgs boson, thereby inducing tree-level LFV Higgs interactions that may be at the reach of the LHC. We study the constraints on the parameter space of the model from low-energy LFV processes, which are then used to evaluate the flavon decay widths and the gg → ϕ → τμ (ϕ ¼ H F ; A F ) production cross section at hadron colliders. After imposing several kinematic cuts to reduce the standard model main background, we find that for m H F about 200-350 GeV, the decay H F → τμ might be at the reach of the LHC for a luminosity in the range 1-3 ab −1 , however, a luminosity of the order of 10 ab −1 would be required to detect the A F → τμ decay. On the other hand, a future 100 TeV pp collider could probe masses as high as Oð10Þ TeV if it reaches an integrated luminosity of at least 20 ab −1 . Therefore, the 100 TeV Collider could work as a flavon factory.