What is easy in one garden isn't necessarily easy in another (and vice versa). You'll want to know your soil type and soil pH, if possible.
I would recommend looking into plant breeds from Europe. There are quite a lot.
Also, most plants will require some work (whether it be planting, pruning, fertilizing, transplanting, de-infesting, etc.) Some that you won't have to plant again might be more work than some of the ones you will have to plant again. For instance, if you do fruit trees, pruning them, and figuring out what to do with the branches, can be a lot of work (as can other aspects of care, potentially).
Of course, for plants that grow from seed, and self-sow, you'll either want heirlooms, open pollinated breeds, or those that you can propagate other ways besides through seed. And, if you want the same kind every year, you'll probably only want to grow one kind of reseeding breed per species.
Here's a list of some general plants (not necessarily from Europe) that I would recommend investigating:
- Jerusalem artichokes (AKA Sunroots/Sunchokes; the tubers have a lot of inulin in them, which is great for fermenting, if you like to lacto-ferment stuff—that's one way to up the nutrition of your foods; these are supposed to produce a lot of roots, once they get going; I haven't grown these yet, but I got some seeds of some wild ones to try this year; people usually grow them from the tubers, though, since they're said to be easy to grow that way, and the commercial ones may be sterile or all clones of the same plant—you need multiple plants that aren't clones of each other to get seeds)
- Bunching onions (I recommend Crimson Forest, for its tall greens, and how easy it is to grow from seed; they handle cold temperatures well; they multiply every year, etc.; you might like potato onions, too, if you can find any; again, don't harvest them all; I mostly just use my Crimson Forest bunching onions for the greens, although they do bulb, unlike many bunching onions—so, they've been at least doubling every year; in 2017 they at least tripled, though, if not quadrupled; you'll probably want to divide them when they multiply)
- Garlic chives (they taste like garlic and grow seeds very easily; they can be invasive, some say; regular chives are perennials, too, but garlic chives should spread faster, due to how they seem to produce more seeds)
- Sorrel (although maybe it's not the easiest to sprout, or save seeds from, it is a perennial that grows a lot of greens, and seems to get bigger every year; I grow Green De Bellville; if you want to save seeds, though, you'll need both male and female plants; mine must be all the same sex, since they don’t produce seeds—although they do produce seed stalks; again, it wasn't the easiest for me to get started, but it's very easy to keep once you get it going; sorrel tastes like extra-sour spinach, but the leaves get a lot bigger, and the plants can get at least a few feet tall; you can harvest the leaves when they're huge, and they still taste good and tender, but the big veins may get more fibrous; they tolerate the cold well, and there's a good harvest window for them, both in the spring and in the fall—I recommend pruning the plants to the ground around the time the summer ceases to be hot, because if the plants are already big, they're probably not going to grow much, unless you prune them; a packet of seeds isn't very expensive)
- Ground cherries and tomatillos will self-sow easily, if you like that. Ground cherries are considered a super food (at least the Cape Gooseberry kind, which is a little harder to grow, but the plants have furry leaves and are very nice-looking)
- Wonderberries (although Wonderberries are pretty small, they do produce a lot of fruits, and they are both pretty early and easy to grow; they're easy to harvest—and you don't have to husk them like you do ground cherries; I'd be surprised if they didn't self-sow, considering the number of seeds per fruit, how easily they drop when disturbed, and how many fruits there are; last year was my first with them, and it's still winter; so, I'm still waiting to find out)
- Mulberries (These are trees, but should be fairly easy to grow, and white mulberries are definitely a super food; the immature leaves can be used, too; they may have extensive roots that can break up sidewalks and such, though; so, give them space; for smaller mulberries, you might try weeping mulberries, or dwarf mulberries; I haven't grown mulberries, however, but they're sufficiently interesting from what I've read that you might want to try it)
- Goji berries (These shouldn't be too hard to grow in France compared to some areas, but they're probably not the easiest thing to grow on the list; they're definitely a super food, though—both the fruits and the leaves; they're perennials; I've never grown them; they're in the Solanaceae family like peppers, tomatoes, tomatillos, eggplants, ground cherries, etc. You can grow these from seed, but they'll take longer than plants; I'm not sure how expensive the plants are)
- Large-seeded sunflowers (These are easy to grow and have a lot of uses. Note that they may cross-pollinate sunchokes. They should self-sow, if you let them, unless the birds eat all the seeds.)
- Amaranth (Definitely a lot of nutrition, particularly protein, in the leaves and the seeds; it grows as a weed in my area, but I've heard the cultivated kinds are easy to grow, too—and they can be pretty showy—but you probably want to focus on those that produce a lot of seeds; some varieties should self-sow easily, but they're not perennials)
- Radishes (particularly De 18 Jours, which only days 18 days to mature; radishes germinate really easily, and they're good at producing decently sized seeds, which can self-sow easily if you let them—so be sure to plant some extras for that, the first time, and don't harvest them all every year; radishes are great lacto-fermented, too, by the way; make sure they get enough sun, and some decent soil)
- Rhubarb (if your area gets cold enough winters, this is one to try as a perennial; just eat the stalks—not the toxic leaves; if you have a friend with rhubarb, they might share some with you to plant)
Even though you may not want to, I'd recommend trying some things you'll have to replant, like zucchini, early, prolific tomatoes, and melons (there are a number of European melons you might enjoy), etc. Some tomatoes will reseed, though. Seed-saving isn't all bad. You don't have to purchase new ones, even if you have to replant. If you're not sure how to save seeds, it's not as hard as some people make it out to be. Just do it—but here are some hints to make things more successful: dry your seeds on or in brown paper bags (or in empty herbal tea bags or some such), in a room with a box fan going. They should dry fast without molding. A lot of people advocate fermenting for some kinds of seeds before you dry them (tomatoes and watermelon especially), but there are other things you can try that might be easier and less smelly, if you do anything special at all (the purpose of fermenting is to filter out non-viable seeds, disolve the sacks around the seeds that may contain diseases and/or enzymes that are said to inhibit germination, reduce disease risk, etc.) You can still easily grow plants from seeds that aren't fermented, though, as I've learned from experience (but disease may be more likely, and if you don't remove the sacks, they may not be as pretty). Some people plant their watermelons just by spitting the seeds in the area they want them to grow the season before when they eat the fruits (that might not work out every single year, but it can be great some years; I don't recommend doing that with grocery store watermelons, since it may be illegal, due to patented and/or PVP breeds, or laws about such, however).
Note: This answer is sufficiently different from my old one that I deleted the old one (which didn't really answer the question, whether or not it initially did) instead of editing it (the people who upvoted the old one may or may not agree with this one).