If you require simultaneous access to the data then using a file-based model isn't going to work. You need a database capable of managing the access. Microsoft SQL server (if you already have one), or any other multi-user database (MySQL, Oracle, etc.) would be your best choice. Microsoft Access is capable of multi-user operation but it requires that the database be split into a cline/server operation -- and that means installing Access on each computer (which could be costly) and installing MS Office products on a server is (I believe) supported. You'd still have to install software on individual computers to get the SQL database drivers.
Another way would be to use a web server to do the work. Installed on a SQL server the driver software wouldn't be required on the clients. You'd have to rewrite the code you're using now, and write more code to run on the web server, but you wouldn't have to install any software on the clients.