We report quantum interference effects in the electrical conductance of chemical vapor deposited graphene nanoconstrictions fabricated using feedback controlled electroburning. The observed multimode Fabry–Pérot interferences can be attributed to reflections at potential steps inside the channel. Sharp antiresonance features with a Fano line shape are observed. Theoretical modeling reveals that these Fano resonances are due to localized states inside the constriction, which couple to the delocalized states that also give rise to the Fabry–Pérot interference patterns. This study provides new insight into the interplay between two fundamental forms of quantum interference in graphene nanoconstrictions.