The traditional arms of France. Since the late 12th century the arms of France were "Azure, a semis of fleurs-de-lis or" - golden fleur-de-lis scattered on a blue background. In 1376 it was changed to "Azure, three fleurs-de-lis or" - just three fleur-de-lys arranged two and one. Ignoring the French Republic, heralds around the world refer to these two variations of the French arms as "France ancient" and "France Modern".
Until 1801 the Kings of England claimed the French throne. Since France was regarded as the senior kingdom, they quartered the arms of France and England with France in the first quarter. When the French kings changed their arms, the English kings did the same thing (around 1405). The arms of France modern still appear today in the full achievement of arms of Canada - twice. See below left.
The personal French royal arms were the same, except with a white (technically silver) background. Showing gold on silver was a deliberate breach of heraldic convention, emphasising that the king was above all human law (the Kings of Jerusalem did the same, and so did the popes - as they still do even today).
The medieval crown was open and decorated with fleurs-de-lis From 1515 representations show a closed crown. Previously only the Emperor used a closed crown). and it may be that the reason for adopting a closed imperial crown was the ceding by Andreas Paleologue (1453-1502), nephew of the last emperor Constantine XI, of his rights to the Byzantine empire to Charles VIII, on 11 September 1494. The supporters were two Evangelists, but from about 1423 they were replaced by two angels.
Click on the following link for more on the Seal of King Louis IX
The Modern Arms of the French Republic. Coats of arms (technically achievements of arms) were associated with royalty and aristocracy, and as such French republicans have always been uneasy about using them. The association with the Ancien Régime is simply too close.
A compromise solution is to use arms that deliberately ignore heraldic convention and that are so mangled that they are hardly recognisable as arms. The emblem on the left is an example. It shows a distorted crescent shaped shield (with a lion's head!) in the centre of the design bearing the cypher FR for République Française (French Republic) - another heraldic infelicity. Until it is pointed out, or highlighted as on the right, you would be hard pressed to notice that the lion headed device represents an heraldic shield.
The symbolism of the other background elements is as follows: