I’m pescetarian. It doesn’t have to be a forced pairing at all.
Personally, I would definitely avoid any seafood (other than maybe a bit of fish sauce if appropriate). People suggesting it don’t get the strong flavor clash from such things that I do, but I promise many people do. Even swordfish would not be a good pairing for me.
Mushroom based dishes are some of the most obvious, and among the best, options. Grilled, sauteed, whatever. I do a vegetarian version of Coq Au Vin where I use tempeh instead of chicken, soy sauce, and extra butter. Something along those lines (red wine reduction with mushrooms) would work extremely well.
I would avoid eggplant because it’s very bitter, and that bitterness, even for those who like it, would tend to reduce the impression of fruit in the wine, which is bad for aged Bordeaux.
Almost anything that has a good base of well cooked onions and garlic will have a nice savory component that helps with the pairing. If they are okay with some carbs, a lentil dish could be a great choice. Something with lentils and root vegetables and that onion/garlic base could be great. I would’t do Indian flavors, but most lentil dishes with a more European flavor palette (herbs de Provence and maybe some lemon juice and salt, for example) would be great with aged Bordeaux.
If you aren’t used to cooking vegetarian food, and you want to do the cooking, I would suggest finding a good recipe. It isn’t always intuitive for people who are used to making meat based dishes. There’s a lot more that has to happen to develop flavor in many cases.
I also have a couple of possibly more simple ideas. Most sorts of creamy, cheesy, or buttery pasta dishes would work well. There are so many options there. I wouldn’t go full on red sauce, but something that includes some tomatoes is good. Also, a vegetarian pizza is often a great pairing if you avoid artichoke, pesto, and hot pepper. A simple Margherita would work great, as would many other pizzas.