Sorry, I don't know a CRM adapting to any database design, it's typically vice versa, even CRMs open for extensibility and offering an API will require you to use their database directly or indirectly.
Just think about how things are coded, perhaps over the top of your head, if you never programmed something. Use of databases means queries, no matter if hand crafted or generated, they depend on a certain table structure, names of tables and fields, types and relations, maybe even triggers. You can't just attach any database, even though it has all necessary essential info for a CRM.
And there's another reason nobody being sane can give you a recommendation for a CRM: You don't tell anything about the size of your company and database. With just a couple of customers some systems are perhaps good enough, but with a rising customer base, you may need more sophisticated features. That's not just a problem of scaling well with the number of customers.
This is not like asking for a good hard drive or choice of Intel vs AMD CPU. This decision is not a merely technical one, it's a business decision and only you know your needs, so you canÄt delegate the decision for a CRM to anyone else.
What you will need, if your own applications process customer data, too, is either a full migration to let the CRM take over that part of your application features, too, then do away with your customer related tables and application features. Or you have to establish a two-way ETL process from your database to a CRM system database or API to keep CRM data of a CRM system and your database in sync. For that to be possible you need a CRM that is open about it's data, but it's not that kind of openness to let itself be adaptable to any database, in the first place it means to allow connections to its database in the first place. A system you rather use in the cloud as a service will likely not offer direct CRM database access, but access via web services or a Restful API, which would need to be used to write and read data to it. That'll be a costy module just to adapt your own data and CRM system data, but it may be worth it.
So you missed a past decision to look for a CRM system first and adapt your own development to the way the CRM needs its data. It's also a reason for the success of ERP systems like SAP, if a company is bigger. ERP systems don't just cover one topic like a CRM or a PLM or a Shop system, they cover the whole business.
Bye, Olaf.