Into Frankfurt, out of Zurich Christmas time

Are you leaving 3 or 10 days later?

These are the many markets that are all close to Frankfurt, some of them are just on a weekend, and some of them are in charming, quaint towns. In case you find the idea of sitting in a train for another 3 hours after a trans-Atlantic flight to be a bit much.
21.11-23.12 Rüdesheim
25.11-22.12 Frankfurt
25.11-22.12 Heidelberg
25.11-23.12 Fulda
25.11-6.01 Speyer (24th 10-13:00, closed 25-26)
26.11-23.12 Wiesbaden
28.11-22.12 Aschaffenburg
28.11-23.12 Mainz
29.11-22.12 Hanau
29.11-22.12 Michelstadt
29.11-23.12 Marburg
29.11-23.12 Limburg

Small Markets/Weekend Markets

25.11-22.12 City Forest, Frankfurt
26.11-22.12 Rosa Market, Frankfurt
28.11-1.12 Oberursel
29.11-1.12 Bad Homburg
29.11-1.12 Swedish Mkt. Frankfurt, an der Wolfsweide 54
30.11-1.12 Ronneburg Castle
30.11-1.12 Hessen Park Open Air Museum
4-8.12 Büdingen
6-8.12 Idstein
6-8.12 Hochheim
6-8.12 Latin America Mkt. Frankfurt, Bockenheimer Warte
6-8.12 Königstein
6-8.12 Bad Homburg
6-22.12 Alt Sachsenhausen, Frankfurt, 16-23:00
7-8.12 Hofheim
7.12 Kronberg
7-8.12 Ronneburg Castle
12-15.12 Gelnhausen
13-15.12 Bad Vilbel
13-15.12 Bad Homburg
14.12 Eppstein, 15:00-22:00
14-15.12 Rewe Markt, Hessen Park
14-15.12 Ronneburg Castle
20-22.12 Bad Homburg

City Alm – 1.11-30.12 open 17:00-00:00 M-F, 12-00:00 Sat., 12-22:00 Sun.
This Food & Drink Christmas market is on top of the parking garage behind Peek & Cloppenburg and offers the best skyline views.

3 days. Just a weekend trip.

You haven't said your actual dates. Given that most Christmas Markets start the last weekend in November, and most end Christmas Eve midday, I hope your dates are OK.
Given your flight into Frankfurt and out of Zürich, Munich is too far. Munich to Zürich by train is slow and wastes too much time.

Mrs Jo has given you a good list of the ones near Frankfurt, but seeing as you want to end in Zürich, you need some options further south:
- Strasbourg. One of the best if not the best. Must be included. And easy by train from Frankfurt and to Zürich Website: https://noel.strasbourg.eu/en/accueil
- Freiburg im Breisgau. Website: https://weihnachtsmarkt.freiburg.de/
- Colmar. Smaller. Website: https://www.noel-colmar.com/en/colmar-the-magic-of-christmas/five-christmas-markets
- Basel. Yes, my local one, but I still think it is very good. Largest in Switzerland. Website: https://www.basel.com/en/Christmas-in-Basel/Christmas-Market
- Lots more smaller ones (Luzern, Zürich, . . . )

Thursday morning into Frankfurt, and leaving Sunday from Zurich

Disaster, only 3 nights. The markets are best after dark.
And what times are your flights? Do you have much time on the first and last days?
My suggestion:
- Thursday afternoon/evening Frankfurt market + overnight
- Friday train morning train to Strasbourg, overnight
- Saturday morning train to Basel, overnight.
- Sunday, depending on when your flight is, train to Zürich and fly out.
That gives your 3 markets in 3 countries

Ah, thank you - I was not aware of the strike. That will definitely affect my plans.

I was going to try and avoid driving, but... if the train strike does happen, would renting a car be a better alternative? For that matter how long is the train from Munich - on the DeutschBahn website it looked like a direct and only 5 hours.

Just to make sure you understand -- the strike is French trains, not German or Swiss. As AshleyMIA noted, there are German (DB) trains that can get you to/from Strasbourg easily. (This will be our second Christmas markets trip to Strasbourg -- great place!)
Also, if you have a connection at the Zurich Hbf, they had a mini-Christmas-market right in the station.

It gets dark at 4:30 in Germany at Christmas and it will be cold. Have a heavy overcoat, hat, gloves and warm shoes or boots.
Also, going to Zurich, you may run into snow.

Renting a car in one country and returning it in another has a big surcharge. Renting in Frankfurt airport and returning at Zürich airport is not financially practical.

As the others say, it is only SNCF (French Railways) that is going on strike. I do not know if this will affect the Strasbourg - Basel trains.
Frankfurt - Strasbourg is a German train and will not be affected, Basel - Zürich airport is Swiss and is equally not affected.
The options are:
1) Hope the Strasbourg - Basel trains are running. With (2) as a fallback.
2) Strasbourg to Basel via Germany. This takes longer than the direct route.
3) Do Frankfurt-Freiburg-Basel. This avoids France. However IMHO I think Strasbourg Christmas market is the better one.

I was reading a little more on the strike, and it sounds like there will be lots of support - Air France ground crew likely to support it, and I am not counting on local transit to run much, either. I am still tempted by the train from Munich to Zurich, looks like it leaves a little after 12 and arrives a little before 5pm. I am not sure how scenic that stretch of the route is, but it will give me some sightseeing time.