TGV reservation from Dijon to Basel

I don't which site you are using, "TGV website" is ambiguous. Try: https://www.captaintrain.com
A lot more user friendly. They will sell you a ticket you can print at home, at the same price as the SNCF (French Railways) website. You don't want "pick up tickets", that means you pick them up at the station in France.

Technically you are not travelling from one country to another. Basel is the last SNCF station, so this is purely an SNCF domestic train, as far as Basel.

It may be the same price, but there is one level of lowest intro rate that Rail Europe doesn't have, called "Prems" if you are booking far enough ahead to get that. To stay on voyages-sncf, choose France. You can change it to English at a later step. See also https://www.ricksteves.com/travel-tips/transportation/trains/france-rail-passes#ticket-tips.

Sorry, I should have been more specific - yes the SNCF website - just looking for a TGV train. Ok, I'll look at your suggestion - thanks!

Also, how much time should I give between connections at a station like Dijon or Basel?

Thanks!

Pumpkin,
If you are looking up times on the internet, this has the minimum connecting time programmed in. You can allow more time. The German railways site www.bahn.de (which has timetables for most of Europe) allows you to add extra time.
In some cases trains stop side-by-side on opposite sides of the same platform, so 5 minutes is easy. If you have to go down-across-up to another platform allow 5-10 minutes. That is assuming you can walk briskly and are not lumbered with luggage or slow-moving grandparents.

Basel SBB station, which I know well, I would recommend 10 minutes for first time visitors, in practice 5 minutes should be enough. All platforms are parallel, and all are connected to a cross passageway by escalators. EXCEPT if you are coming from a terminating train from France. these stop in an annex and I would then allow 15 minutes for first time visitors.
A plan of the station is here: http://www.sbb.ch/content/sbb/de/desktop/bahnhof-services/am-bahnhof/standort/bahnhof-baselsbb/_jcr_content/relatedPar/contextmenu_1/downloadList/bahnhofplan_.spooler.download.pdf

I am not familiar with Dijon station.

Chris F. - you have been very helpful - thanks!!

Dijon I would characterize as a medium size station (although surprisingly the platforms are out in the open so if there's weather, beware). Very simple to use.