  Monolayer FeSe grown on SrTiO$_3$ provides a new playground for high-Tc
superconductivity. A recent study shows the importance of stripy instability
for superconductivity enhancement in FeSe/SrTiO3. However, it is still under
debate whether such a stripe phase is ubiquitously bound to the interfacial
superconductivity. Here, we report on molecular beam epitaxy growth and
low-temperature scanning tunneling microscopy study of FeSe films on
BaTiO$_3$(001). We find that the stripe phase is more prominent in
FeSe/BaTiO$_3$. Long-range stripes exist in bilayer and triple-layer FeSe films
at 4 K and even persist up to 77 K in the case of bilayer FeSe, with enlarged
superconducting gaps upon alkali-metal deposition. The results point out an
intimate correlation between the interfacial superconductivity and the stripe
phase.
