This disc I intended to give to someone else so that he and his family could watch it together.
Try making an educated guess. Will they be wanting to play this on a set-top DVD player (or Blu-ray player) connected to a TV, or will they be playing this from a USB stick in a TV, or will they be playing this on a computer? The latter two options make it much easier on your part (no authoring needed).
Besides VLC Player, which I don't think either downloads or burns, my other apps look like they can only download.
VLC is mainly just for playback of media files on a computer. Its strength is that you don’t have to worry about what types of files those are. It can do a bit more than this core functionality, but I don’t think that applies for what you are aiming to do.
If you want to burn to disc, for something playable in a set-top player connected to a TV, then you’ll need DVD/Blu‑ray authoring software. Others have mentioned examples in this thread, and any of those are fine. As ‘Burn’ is free and not complicated, first see if that does what you need or expect from a DVD disc. You can always decide to put more effort in with fancy menus and more elaborate software, but you may not need that for this project.
With the term “authoring”, we mean preparing for the very narrow specification of requirements as needed to be able to burn a valid disc (for a playback on a set-top player). Preparing with the frame size (width and height in pixels), and frame rate, codecs, and other video and audio parameters that the format requires. Quite often, this necessitates a conversion from the source format. Authoring software can help automate this process, as it knows what is needed.