Front's Core API lives at https://api2.frontapp.com.
Create a key at Front → Settings → Developers → API tokens. Send it as Authorization: Bearer <key>. In the examples it's written {{FRONT_API_TOKEN}}.
Full reference: https://dev.frontapp.com/reference/introduction
curl https://api2.frontapp.com/me \
-H "Authorization: Bearer {{FRONT_API_TOKEN}}"
curl https://api2.frontapp.com/inboxes \
-H "Authorization: Bearer {{FRONT_API_TOKEN}}"
curl "https://api2.frontapp.com/conversations?limit=10" \
-H "Authorization: Bearer {{FRONT_API_TOKEN}}"