@JeroenAruba
There are a lot of considerations to evaluate before decided on how, and even if, you want to try to use this Access Relational Database Application "on the internet". Not the least of which is, what you actually need to do that requires an internet component.
First, Access runs under the Windows operating system on a computer. That means it can not directly be deployed to the internet. Microsoft actually tried to do something like that at least twice and failed both times.
That said, there are alternatives which allow remote users (i.e. users not located on your premises and using computers connected directly to your LAN).
One is to move the data from the ACE engine in Access to a hosted database or to SQL Azure or some other RDBMS hosted "on the internet". That allows users to connect to the shared data from any computer with your Access relational database application's Front End -- or interface-- over the internet. The key, of course, is that the data ONLY is in the cloud.
Another is to deploy a Remote Desktop solution in which your users can log in to a computer inside your network via remoting software (LogMeIn, is one such application, but there are several). This can be a low-cost and effective way to make the relational database application available to remote users.
A third approach would be to locate a service that promises to host your Access application as a "cloud application". I know of one or two, but have no experience with them or the approach so can't comment further.
Another approach would be to create a sort of "hybrid" application. Your data would, again, have to migrate from the local network to a cloud or internet accessible location such as SharePoint lists or a SQL Azure or hosted SQL Server database. Then, your internal users continue to use their Access Front End interface linked to that data as always. However, you can use MS PowerApps to create small, narrowly focused apps that run in a browser on on a smart device to work with some portion of the data pertinent to their needs. E.g. a real-time ability to look into an inventory table while sitting in a potential customer's office.
Others will be along to offer suggestions, and perhaps deeper dives into one or more of these alternatives. Do your own research and see what you turn up that might suit your budget and requirements as well.
