  The reaction between He$^+$ and CH$_3$F forming predominantly CH$_2^+$ and
CHF$^+$ has been studied at collision energies $E_{\rm coll}$ between 0 and
$k_{\rm B}\cdot 10$~K in a merged-beam apparatus. To avoid heating of the ions
by stray electric fields, the reaction was observed within the orbit of a
highly excited Rydberg electron. Supersonic beams of CH$_3$F and He($n$)
Rydberg atoms with principal quantum number $n= 30$ and 35 were merged and
their relative velocity tuned using a Rydberg-Stark decelerator and deflector,
allowing an energy resolution of 150 mK. A strong enhancement of the reaction
rate was observed below $E_{\rm coll}/k_{\rm B} = 1$~K. The experimental
results are interpreted with an adiabatic capture model that accounts for the
state-dependent orientation of the polar CH$_3$F molecules by the Stark effect
as they approach the He$^+$ ion. The enhancement of the reaction rate at low
collision energies is primarily attributed to para-CH$_3$F molecules in the
$J=1,\,KM=1$ high-field-seeking states, which represent about 8\% of the
population at the 6~K rotational temperature of the supersonic beam.
