Getting data from Firestore in the cloud to local can be done using a paid app such as FireFoo or from the command line using the cli tools provided by Google.
I’ll assume you have the firebase CLI installed as you have the emulator already. The gcloud tools are available for nearly all platforms.
Once you have them setup, run the initialization
gcloud auth login
Make sure you are using the right projects. For firebase you are most likely setup but you can check with
firebase use your-project-name
The command for gcloud are similar
gcloud projects list
gcloud config set project your-project-name
now do a backup if you have not already
gcloud firestore export gs://your-project-name.appspot.com/folder-name
cd into a temp folder and download with a copy command.
gsutil -m cp -r gs://your-project-name.appspot.com/folder-name .
Make sure the emulator is not running and copy those contents to over the existing files in you emulator folder.