As pointed out in my comment on the question, I cannot tell for the "Nautilus" requirement.
You've explicitly asked for a graphical file explorer – so I will first answer your request literally. For my really recommended solution, see the end of this post :)
QtADB is probably the best known application in this context:
QtADB file manager and app manager (source: QtADB; click images for larger variants)
It seems to match your requirements:
- No app needed on the Android side (I have adb installed if that can help): Check. ADB is required, but no additional app on the device.
- Graphical UI: Check, see screenshots above.
- Ability to put/pull files to the local Ubuntu filesystem: Check, see first screenshot.
- compatible with Nautilus copy/paste or mouse moves: As initially stated, I cannot check this.
- Free, ideally open source: Definitely free. And since 2011 also open source.
To name an alternative: aafm is a very simple Python based file manager for the command-line and GUI:
aafm file manager (source: aafm; click image to enlarge)
I've never tried this one, but it should match your listed requirements the same way (license: GPLv3).
But now for my real recommendation. Interpreting your question as if you'd asked it at Android.SE ("How can I …"), I'd recommend you taking a look at adbfs-rootless – which I am using happily. This works as a FUSE mount, and thus your Android file system is available everywhere – no need for a separate file manager, should integrate in whatever file manager you're using as if it belonged there. Thus it really meets all your requirements:
- No app needed on the Android side (I have adb installed if that can help): No app needed on the Android side (I have adb installed if that can help):
- Graphical UI: up to you. If you have a graphical file manager, which you do: Check :)
- Ability to put/pull files to the local Ubuntu filesystem: Check. Copy as you would do locally :)
- compatible with Nautilus copy/paste or mouse moves: If you use Nautilus, I don't see why not :)
- Free, ideally open source: adbfs-rootless uses the BSD license, so: Check.
You most likely even can configure a Nautilus shortcut to mount/unmount your Android device for easier use.