I do not believe you can purchase this prized variety in the U.S. A similar variety is ‘Mara des Bois’ -- introduced by French nurseries back in 1991. Google this variety and you'll see U.S. nurseries that sell it.

Do not plant strawberries where tomatoes have been grown in the past four years. Tomatoes--as well as potatoes, peppers, and eggplants--carry the root rot fungus Verticillium, which attacks strawberries.

To rejuvenate the strawberries leave some of the younger plants that grow from the runners and discard the mother plants. It's going to be hard to identify the variety. (You can go to farmer's markets and taste the strawberries sold to see if you can match the look and taste of your strawberries.)

In Texas, strawberries are best planted in the fall but retailers seem to sell them in the spring. Just make sure that 1) the soil stays moist and well irrigated, 2) the plants are protected from any dry winds, and 3) the soil pH is not too high (6.5 to 7.0 is ideal and amend with compost or peat moss if needed). At planting and periodically, add a balanced fertilizer. In the fall/winter, after a couple frosts, go ahead and mow down the runners. Then throw super-phosphate over the patch. Next spring, spread some 10-10-10 over the area before new growth begins. If their production doesn’t improve, dig them out and replace with a new planting. In Texas, sometimes cultivated strawberries (not wild ones) are treated as annuals.

You might want to reconsider your strategy. Removing the flowers when they first appear in the first growing season promotes root development and thus ensures a large crop the following year.
If that time has passed, you could try it in this growing season, or "renovate" the crop now. This means cutting the foliage with a mower (or perhaps scissors in your case), removing the foliage to about 1 inch above the crowns. This puts the energy of the plant back into the ground; it doesn't waste energy growing a "top." Clear away the clippings, then fertilize with 10-10-10, weed well, and water with an inch of water per week. Finally, leave the runners alone. Every resource we know if says that you want runners. Replant the beds with new plants every three or four years. We hope this helps.

I'm not sure if strawberries will grow well in a topsy turvy planter, but you can grow strawberries in a container.
Any small ever-bearing strawberry variety (like the alpine strawberry, or wild strawberry) is a good choice because you don't want the berries to get too big or heavy. When planting, start with small young plants. They are easier to fit into the plant pockets, and their root systems will quickly spread inside the container. Use a well-drained potting soil. Make sure you plant the strawberries outside after any danger of frost has passed. You also can start the plants indoors earlier if you like.
Hope this helps! Good luck.