If you want to reload after file changes, you can run Parcel in watch mode, which compiles changes to another directory (default ./dist/) but does not run a server.
parcel watch index.html --no-hmr
Then run a live-server, which listens to file changes and reloads (assuming your output is to the ./dist/ directory)
live-server ./dist/
Here's what my npm start script looks like:
parcel watch ./src/index.html --no-hmr & live-server --port=8000 ./dist/