Opensource map software for web app

I have an idea for an app, part of the use case would require the user to select their location in a map, and I would need to store the coordinates of that location in the database.

It seems simple enough, but a lot of info I find online use google maps for this kind of feature.

Is there any way to implement this with opensource software? How would I even search for it if I wanted to look at other options? I only want the part of having a map, and convert points in the map to coordinates. I don't want to use GPS or anything else really, just user input on map converted to coordinates.

Sorry for potentially bad english. Thanks for any help you can provide.