By "train", I am not sure if the OP means "rolling stock" or "route/time/number in a timetable". I can't say much about the latter, but regarding rolling stock:

France
The first TGVs were introduced in the 1980s. The TGV Sud-Est was introduced in 1981, but I'm not sure if these are still in operation anywhere (I understand that TGV Lyria have just phased out the last few they were using). The TGV Atlantique was introduced in 1989, and I assume these are still in operation.

Germany
In Germany, the high-speed ICEs that now operate the key mainline routes were only introduced in 1991. However, some of the ICs that operate other mainline routes may be 1980s era rolling stock (although unlike Aviatrix, I haven't noticed any unrefurbished stock).

In Bavaria, the regional ALX services use relatively old (I'm guessing 1980s) rolling stock, although the interiors have been extensively refurbished. They also have a couple of 'museum piece' restaurant cars from (I think) the 1960s, which are still in regular use (although only with a limited offering of drinks and snacks - the full catering kitchen is still there, but sadly not used any more ). And, somewhat incongruously, many of the ALX trains also have 1 modern double-deck carriage attached as well!

Although not mainline services, a number of narrow gauge railways in eastern Germany (eg: Harzer Schmalspurbahnen and Zittauer Schmalspurbahn) are still operating, with rolling stock (and steam engines) that have been in service since long before the 1980s!

In Czech and Slovakia, there are a number of sleeper and couchette carriages and (at least in Slovakia) seats carriages still in mainline service that were built in East Germany in the 1980s. However, I am not sure if these particular carriages ever saw service in East Germany, or whether they were built for direct export to Czechoslovakia (although I assume that similar models were indeed used in East Germany).