This train has 68 places in 1st class but german carrier DB (https://int.bahn.de/en) does indeed show that 1st class is already sold out for your given date. 

If you'd like to go 1st class you might choose another connection with change in Mannheim.

ICE 563 is just sold out in 1st class from Mannheim to München so it would even be possible to get a reservation from Homburg to Mannheim for this train and change there to an other ICE. But there are many other connections with one more change in Mannheim throughout the day.

(One day earlier or later 1st class is available for the direct train.)

(All ICE are fixed trainsets (even if there are different ICE types). But there's no ICE without 1st class.)

Thank you very much for the reply, since I am going on to Vienna, I found another connection via Frankfurt. Taking Regional Express RE3 from Saarbrücken to Frankfurt arr 10:48 and ICE from Frankfurt to Vienna departing 12:22, where 34 minutes in Frankfurt for changing should be plenty of times.

How can I find on DB what seats are available on ICE trains. I too tried with eurorail to book from Homburg to Mannheim and it didn’t give me a 1st class option.

Thanks

Horst

Of course it's less comfortable to go from Saarbrücken if you'd like to go from Homburg. Also be aware that the RE to Frankfurt is just a vlexx regional train with uncomfortable 1st class (in fact the same seats as in 2nd class with a little bit more legroom).

If you do follow the link given before and scroll down on that page, you do find "book seats only". But it's 5,90 € per person to book with them - but connecting trains are free of charge when not going over the border into Ausrria).

From Homburg, there's an early connection with just one change at 5.57.

I tried this one already, but didn’t finish the booking so when will it show if it booked the 1st class tickets or what is available in 1st class?

Eurorail does not show 1st class from homburg to Mannheim

Got it even to Mannheim fully booked on 1st class

You need to tap "1st class" even before searching for the connection. 

You may see it even when checking the price. 2nd class reservations are 4,90 € per person, 1st class reservations 5,90 €.

(For a single train it's cheaper to book with austrian carrier ÖBB; just 3 € per train.)

I do get a seat reservation for June 20th - but of course I didn't try to pay for it.

But Homburg to Mannheim is even just 1 hour with reservation-free RE that runs about every hour so no problem at all (or the direct train to Salzburg at 5.57).

I did it and it came back that it is fully booked. just booking my Frankfurt to Vienna with DB, which I found is cheaper than eurail

It's cheaper with ÖBB - 3 €.