Final answer:
The Flamboyant Style is a development of the French Gothic style characterized by flamboyant tracery and ornamental detail, as seen in buildings like the house of Jacques Coeur and Southwell Minster, which transitioned from High Gothic to Rayonnant Gothic styles.
Step-by-step explanation:
The development of the French Gothic style featuring increasingly flamboyant patterns of repeated traceries and ornament is known as the Flamboyant Style of Late Gothic architecture. Notable examples include the house of Jacques Coeur in Bourges, France, and the Southwell Minster in Nottinghamshire, England, where the intricate stonework and tracery became more florid. This period followed the High Gothic style, exemplified by Chartres Cathedral, and evolved into an even more decorative phase with slender columns and larger windows allowing for more light, culminating in ornate structures such as Gloucester Cathedral.
The term 'Flamboyant' derives from the flamelike appearance of the ornate tracery often found in the vast window spaces of these Gothic buildings. As exemplified in the Cathedral of Notre Dame de Paris, which underwent several modifications and renovations, the architectural style continually evolved, leading to the Rayonnant Gothic style with its thin traceries, thinner columns, and larger windows. This period of architecture was characterized by its verticality, lightness, and the dramatic use of stained glass.