Contracts for Salesforce connects to your Salesforce organization using the credentials of a user that you choose. It is therefore limited by the permissions granted by that user. The setup page will inspect the permissions of your user and provide a warning if any required permissions are missing.
A Permission Set is provided with the package that grants the required Field and Object permissions needed. If this is applied to all Contracts for Salesforce users, the required and recommended permissions will be satisfied.
You are not required to use the provided Permission Set or a System Administrator Profile if the permissions outlined below are granted to the necessary users.
Salesforce best practices for integration users also calls limiting the user with API only access. This can be accomplished by logging in as the user and connecting to Contracts for Salesforce before applying the API only configuration.