I looked at a variety of websites regarding fertilizing fig trees.
From Univ of Georgia extension service, "a satisfactory amount of shoot growth is about a foot per year."
Clemson Univ talks a lot about fertilizing, but also states that in soils of average fertility, fertilizing might not be needed. They also state that too much fertilizer can cause loss of yield, as can too little water.
A website called "The Fruit Grove" discusses fertilizing, but notes that if the trees are already growing and producing well, then fertilization might not be needed and, again, too much - especially nitrogen - can reduce fig production and cause rank, non-hardy growth that is more susceptible to winter kill.
I can't find the reference right now, but another said don't fertilize if there is more than six inches of growth.
I checked how long new growth was from last year.
A lot of new stems are six to nine inches. Some are longer, and Violette de Bordeaux (as noted earlier, probably falsely sold as Petite negri) always has less growth, being dwarf in habit ( I think brachytic dwarfism = short internodes).
Considerations -
I almost always get more figs than I know what to do with anyway.
I normally don't fertilize my fig trees. They usually do fine without.
American and worldwide fruits and vegetables have become significantly less nutritions, as well as less flavor, over the past 70 years. Part of that is fertilizing depleted soils to boost yields and speed growth.
Sometimes I have spread wood ashes in the fig grove. I don't know if that is fertilizing or just soil building.
The fig grove is also a "rest stop" for Rufus. It actually gets quite a lot of fertilizing via doggie. That the grasses there are the lushest and fastest growing in the yard, probably indicates that is enough.
My aim is quality, richness of flavor, and while I might not see or taste it, nutrition. Raising yields, and growing even bigger figs, just isn't on my wish list.
So after all of that, I decided not to fertilize the fig grove. After the next grass cutting, I'll cast a dusting of wood ashes. The added calcium as well as other minerals should be beneficial without causing rank, weak, overgrowth.