The program is free and open source, but there is no combination of program and library, and the program itself may not work. It depends on what the library actually does, and how important it is to the functionality of the program.
If this is a library that is part of the operating system or is usually installed on your users' systems, users will already have it, and you will give them the FOSS program, like any FOSS application that runs only on Windows (for example, Miranda) or the FOSS plugin for a larger proprietary program.
Another case is when you have an additional function for interacting with a proprietary application in the system, for example, the FOSS communication program, which has functionality for accessing the address books of third-party applications, including proprietary ones, such as Outlook. In this case, the library is not required at all for the core functionality.
If, however, you create a stand-alone program, the main functionality of which depends on the proprieatry library (for example, all the functionality is in your own library, and only the GUI is FOSS), your application will be FOSS in theory, but not in practice, because the library is integral part of your application that cannot be removed.
Please note that you are likely to violate the GPL if you use any third-party GPL code or libraries, unless your own library is part of the operating system. Therefore, do not use third-party GPL code and third-party native code together. (Of course, if you do not distribute the library of third-party developers or use only your own code, this will probably be legal, but you would create a combination of software that would be illegal for distribution in working form.)