I got asked just this week by a learner what was the difference between Ultramarine Blue paint and French Ultramarine Blue?
The short answers is not a great deal. In the early 19th century the cost of ultramarine made from lapis lazuli was much higher than any of the other pigments, so much so that some artists did not use much blue in their work if any.
Two French chemists discovered some blue residue in a soda furnace one day and wondered if this could be developed into a blue paint to replace the costly ultramarine pigment. After lots of development work an alternative was developed which was cheaper and soon came into production. In order to differentiate it from the lapis lazuli it was called ‘French’ Ultramarine.