His list covers French armies from the outbreak of the Frondes series of civil wars (1648-1653) until Louis XIV took over personal control of the government after the death of Cardinal Mazarin in 1661, which allowed Louis to dictate military matters.
During most of this period the French were at war with the Spanish in the Low Countries and, to a much lesser extent, in Catalonia. In addition, from 1648 to 1653 there were a series of civil wars in France, which are known as the Frondes - from fronde, meaning a sling, which was used by rioters in Paris at the start of the first civil war.
The Frondes were notable in that the two best French generals, Turenne and Conde, were both in opposition to the government of Cardinal Mazarin and the Queen Mother, Anne of Austria. However, in 1650 Turenne, realising he was being manipulated, asked for a pardon from the young Louis XIV, which he received. He then led the Royal armies to defeat the rebels, whilst Conde actually entered Spanish service.
The war with Spain was finally decided following the Spanish defeat at the Battle of the Dunes in 1658. The battle saw a French army led by Turenne, with allies supplied by the Protestant Commonwealth of England, face a Spanish army which included French cavalry and infantry led by Conde. The subsequent Treaty of the Pyrenees which brought the war to a mostly satisfactory conclusion for France, also saw Conde pardoned by Louis and re-enter French service.