Is there a train from Germany to Tours... without going through Paris?

Theoretically, yes, but it would be very roundabout and probably take a couple of days as the system is set up with Paris as a hub. Have a look at this map of French rail lines and you’ll see why - https://about-france.com/france-rail-map-hi-res.htm

Yes, quite easily from Stuttgart and from Köln.
From Stuttgart: take a train to Strasbourg, then a direct Strasbourg-Bordeaux. The stop for Tours is Saint Pierre des corps.
You could do the same from Frankfurt but it is more time consuming, sometimes involving an extra connection in Germany.

From Köln: take a train to Brussels Midi, then a direct Brussels-Bordeaux, and same as above.

EDIT: hmmm this looks OK on a random date in June's but somehow the August schedule is different and does not show any good option.
If you have to end up crossing Paris by metro, Est-Montparnasse or Nord-Montparnasse is a straight shot on line 4, should not be too bad.

EDIT 2: the Olympics will be over on Aug 19!

There is no through train, but there are ICE's from Koln to Brussels, TGV to Charles de Gaulle, TGV Charles de Gaulle to Tours (sometimes with a change at St Pierre de Corps, for a TER for the final 5 minute journey.
Total journey time 8 to 9 hours.

Olympics are scheduled to end on 11 August. It should not affect your travel date.