In a library context enquiry/inquiry management is different from most CRM systems which are designed to manage outbound sales and marketing interactions. Enquiry management for libraries is atypically about helping keep track of enquiries, facilitating follow up and maintaining statistics.
The are some general purpose system that might work in a library environment . eg from Evolutive
The Request Tracker (RT) system from Best Practical is an open source option that you can either install and run yourself (for free if you have technical staff) or pay Best Practical to host and/or support for you: https://bestpractical.com/request-tracker
Management of general enquiries in a library can be distinguished from online 'Reference Librarian 'services such as QuestionPoint.
NOTE: "OCLC has entered into an agreement to sell the QuestionPoint 24/7 Reference Cooperative and active
QuestionPoint subscriptions to Springshare, provider of the LibAnswers Platform. 31 May 2019 https://www.oclc.org/en/questionpoint.html