To be honest - there aren't any free alternatives to MS Access. At least if you mean database development tool (forms, reports, queries, VBA support etc.). If you think about MS Access as a database engine (you mean MS Jet or ACE in fact) then yes - you have a lot of possibilities. There are a lot of free database engines - the most popular are MySQL and PostgreSQL. I can recommend both - it depends what you want to do.
For writing database frontends C++ is one of the worst choices. You should consider MS Visual C#, MS Visual Basic .NET or... Even Java/Swing (if we are talking about desktop application). If you think about the web-enabled frontend - consider PHP (with MySQL or PostgreSQL on the backend) or ASP.NET (with MSSQL Server at the backend).
I strongly recommend you not to use C++ for such job. This language is very efficient and flexible, but advanced database frontend development with C++ is not the best idea. C++ is great in system programming, games development, maths and physics simulations, everywhere where efficiency is the key - like real-time applications etc. Frontends don't have to be daemons of speed - they should look nice and have advanced end-user features (like sorting, coloring etc.). If you are looking for free tools - maybe C# Express or Visual Basic.NET Express 2008 would be the proper choice? Or maybe Java/Swing (check the NetBeans IDE)? Maybe SharpDevelop? But not C++... Leave C++ for the things it suits the best.
