In a saucepan of boiling salted water, blanch the snap peas until crisp-tender; using a slotted spoon, transfer to a plate and let cool.
Add the rice to the boiling water and cook, stirring a few times, until just tender, 15 minutes. Drain and rinse under cold water; spread the rice out on a baking sheet and let dry for 5 minutes.
Meanwhile, in a large serving bowl, whisk the oil with the vinegar. Cut the snap peas into 1/2-inch pieces and add them to the dressing along with the rice, cherry tomatoes, cornichons and basil. Toss well, season with salt and pepper and serve.