The line can't just go a few metres across the border. Let's say it connects Dortmund, in the German industrial heartland on the French side of the country, with Chooz, the site of a nuclear plant near the German border. French nuclear plants are evenly distributed around the country [0], so that should be a reasonable choice. That's 250 km.
High voltage transmission costs around €2m/km to build [1] and carries around 2 GW of power [2].
So your line costs €500m to build and makes €13 x 2000 = €26,000 an hour and pays for itself after 20,000 hours or three years.
You might reasonably say you wouldn't expect to capture all of the €13 per MWh in arbitrage profits, and perhaps this disparity was a short-lived aberration. But actually it's not: electricity futures in France are priced €25 cheaper than their equivalent contracts in Germany [3], so you could reasonably expect to capture a good portion of that - if you split the surplus between you, the consumer and the producer you can still get €9.
Of course, one problem with this free money is that your competitors are already doing it. The gap is expected to narrow over time thanks to interconnectors like this, increased generation in Germany, and French nuclear plants going out of service [3]. Still, with increasing electrification of the energy market, this kind of power transmission seems like a good business to be in and a good investment for national governments and grid operators.
[0] https://www.researchgate.net/figure/Map-of-French-nuclear-po...
[1] https://www.researchgate.net/publication/358793859_Cost_of_e...
[2] https://web.ecs.baylor.edu/faculty/grady/_13_EE392J_2_Spring...
[3] https://montelnews.com/news/e15ef79e-2905-41ca-9124-165d7469...