In fact it is not at all clear which version of the FDL is correct~ perhaps they are all to some degree, however, a treatise on the subject rolls out the various concepts at ~
http://www.heraldica.org/topics/fdl.htm
The window below is shown for interest.. and carries the following detail Quote"Stained glass window in the shape of a fleur-de-lys, Bourges cathedral, 15th c. Note the various themes: the Trinity, which the 3 petals were understood to recall, is represented; angels are bearing the shield as they are supporters of the arms of France, the dove descending from heaven recalls the legend of the baptism of Clovis when a dove brought the sacred ointment to Saint Remigius."Unquote.