The Oldest International Rivalry
The first true international match took place in 1872 between England and Scotland.
I should note that there were so-called “representative football matches” between England and Scotland that took place between 1870 and 1872. However, as this Wikipedia article explains, the Scottish team was composed entirely of Scottish players who were based in London.
The first true international match took place between England and Scotland in Glasgow on November 30, 1872.
Unfortunately, coverage of football in the early 1870s was somewhat sparse, as you can see in these contemporary articles:
This article was the best I could find: