I'm trying to book a transfer from Dijon to Basel, but there's no option to book it. I've noticed this on other routes as well. I thought TGV trains must be reserved online. So why is this?
DB Bahn is the group that manages passenger travel within Germany, and is responsible for the managing, ticketing, servicing and running of all German Intercity-Express, EuroCity, Intercity and Regionalbahn trains, and many commuter-oriented urban Stadtschnellbahn (generally abbreviated as S-Bahn) networks within Germany. The group also handles the information and customer service side of the operation.
Presumably as your train is running from Dijon, France to Basel, Switzerland, it may fall on a route not covered by DB Bahn.
Yes, some of the other routes by its partner companies may be included, but there are competitors on the rail network as well, and there's no requirement to have those included on their site.
Indeed, from Rick Steve's site:
The Deutsche Bahn's site doesn't show fares for most trains outside Germany and Austria.
The reason that you see so many timetable results on Deutsche Bahn without being able to book is because the journey-planning engine it uses (known as Hafas) is separate to its ticket booking functionality (Deutsche Bahn's own online "distribution system").
A master pan-European timetable dataset known as Merits is loaded into Hafas and that's what gives the comprehensive timetable information. As per Mark's answer, Deutsche Bahn can only actually sell tickets for journeys that begin or end in Germany (with some limited exceptions which I won't explain here).
The Deutsche Bahn search you linked to is expired (their search results URLs are not "shareable" in that respect) and so I can't tell which times/dates you are searching for, but if you are looking for somewhere else to book your Dijon to Basel journey, you can use my website Loco2 (the below link is for a 20th November search - cheaper prices can be obtained by booking far in advance):
You can also book the same journey with similar prices at Voyages-SNCF (a joint venture between the French rail operator SNCF and Expedia) and elsewhere.
As an aside, I thought it worth addressing this point from another answer:
As of today, I still do not know any European rail operator that offers both comprehensive timetable look-up and good online sales.
Getting access to the Merits timetable data would enable Loco2 to bridge this gap, and this is something we are working on. Like most things in the European rail industry, it takes a lot of time and effort :)
Generally speaking, train booking is complicated and it would seem that some sites were originally designed to provide timetable and connections with booking as an afterthought. As of today, I still do not know any European rail operator that offers both comprehensive timetable look-up and good online sales.
Consequently, sites that have good timetables do not let you book a ticket for some connections that do show up after a search. Many years ago, as e-tickets did not exist yet, sbb.ch/cff.ch already had timetables for all Europe but no easy way to get prices or book a ticket online, even within Switzerland.
Conversely, sites designed to sell tickets (SNCF, NS hispeed, etc.) have generally patchy timetables and might even not show you a train if there is no ticket matching your criteria.
Bahn.de is usually a good place to get timetables. To book you typically have to go to the national site for the country that contains either the origin or destination. For Americans it gets a little more complicated because the SNCF (French national railway) site redirects you to Rail Europe. However, http://tgv-europe.com/en will let you book, as long as you select Antarctic as your ticket collection country.