The site was acquired by the French community in Rome from the monks of the Abbey of Farfam in 1478. The area was full of remains of Roman buildings, including the Baths of Alexander Severus and the Baths of Nero. Pope Sixtus IV (1471-1484) confirmed the exchange uniting various small churches into a single parish in honor of “The Conception of the Blessed Virgin Mary, St. Dionigi (Denis) and St. Louis, King of France” (patron saints of the French nation), and also set up a Confraternity with the same name to manage the area.
In the early 16th century, the Medici family took over. Cardinal Giulio de Medici, later Pope Clement VII, commissioned Jean de Chenevière to build a small round church for the French community here in 1518. Building was halted when Rome was sacked in 1527. In the mid-16th century, with the support from Caterina de’Medici who lived in the nearby Palazzo Madama, a new church was begun. Giacomo della Porta was in charge of the final stage of building and probably supervised designs: he also designed the façade and was assisted by Domenico Fontana. Construction was completed im 1580, and the church was consecrated in on October 8, 1589 by Cardinal François de Joyeuse, the Archbishop of Toulouse.
For reference, a plan of the church is available here