How many barons were there in feudal 10th century France?

Question

Around AD 1000, the king was technically owner of all of France but the land was 'leased' to his vassals: dukes, counts, lower barons, and these in turn leased it to lower barons and knights.

What I don't have an idea of are the numbers in this tree structure. How many vassals would the king have had (ten, twenty, a hundred), and in what ratio of dukes:counts:barons? How many vassals would a typical baron have? Were the dukes as powerful as the king in terms of vassals, ie was the king "primus inter pares"?

Answer 1

No contemporary French record on the scale of the Doomsday Book commissioned by William I is known. However, given reasonable assumptions, good extrapolations for French dominions can likely be made from estimates obtained from this prosopography of the Doomsday Book

On page 23 it is noted:

In the Doomsday prosopography which follows hereafter some 19,500 records of continental names, excluding the king, have been analyzed as 2,468 different people. These include about 200 tenants-in-chief, and about 600 Englishmen.

with the total arrived at as (pp 15):

If one discounts the demesne tenancies of the churches - as distinct from bishops or abbots - the tenancies of Englishmen and those of the king some 19,500 remain.

This provides us with approximately 200 future baronies (the tenants-in-chief) and some 2,468 - 200 =~ 2,268 sub-tenancies. This is then an average of ~11 sub-tenancies per tenant-in-chief.

Assuming roughly equal land fertility for England and France, and given that the area of modern France (~643,000 km-squared) is nearly 5 times that of England (~130,000 km-squared), would yield estimates of approximately 1,000 tenants-in-chief and 11,000 sub-tenants for the area that is now modern France. These latter numbers perhaps help in understanding why it took so much longer for France to unify nationally compared to England.

Update

Evergalo points out below that the area of mainland France is about 20% less at just 544.000 km^2. This reduces the net numbers likewise by about 20% to perhaps 800 tenants-in-chief and 8,800 sub-tenants.

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In terms of the five peerage ranks - Duke, Marquess/Marquis, Earl/Count, Viscount, and Baron - Duke and Marquess were senior positions, with the Marches held by a Marquess/Marquis being border territories otherwise equivalent to a Duchy. The Counties and Baronies held by the junior peers were, originally, typically sub-divisions of the duchies and marches, some of which might be held directly by the monarch and heirs.

Answer 2

During the 10th century, you had 5 dukedoms in France. At the dawn of the Capetian era, you had only 4 left, so in 1000 A.D. you should have 5 dukes, but the title Duke of Franks maybe was still used by the French kings/heirs. One more was added in 1088, and afterwards, lot of them went extinct, merged etc, tough act to follow.

Counts were usually quite low in the social ranking of medieval France, unless they were counts of Flanders, Champagne or Toulouse. Those were peers, but the oldest one I can find is from 1156. So I guess they were not very relevant before that. Barons were very numerous and almost "lowest" noble there was, for a fun fact, a Baronny could be sold to a commonner which then became Lord of the Baronny and not a Baron, the seller would lose its title and no such Baron would exist as long as no Nobles held the land where the seat of power was. Some Barons could hold several baron titles, and in fact, many Dukes and Counts were Barons and Marquis, too. A "typical" baron is thus quite a difficult term. They could be managing a little Fief with maybe 100 people living in it, or managing big regions. Depended on the title (baronies could be very unequal) and if the holder had more titles unders his belt.

The dukes were indeed as powerful and most of the time stronger than the king, it took a LONG time for France to become an absolute monarchy and for dukes to be much weaker than the King. BUT the French king was the first among peers, supposedly.

The dukes of Normandy and Aquitaine under House Plantagenet were the most famous powerful dukes that challenged the French Crown, most notably with the Hundred years war. Before that war, Richard the Lion-Hearted most famously challenged Philippe-Auguste and was considered much more than an equal for the french King. The Duchy of Aquitaine was at one time considered a different kingdom altogether, much richer than the rest of them, when one French King married to the heiress of the Duchy, most people wondered who was the most honored of the two, the Duchess who married to a King or the French who got Aquitaine "secured" ?

Other notable powerful dukes were the dukes of Burgundy, which at one point declared themselve Kings, look for Charles the Bold (and his famous demise). The dukes of Brittany were very important for the French Kings and were maybe the "loyalest" of Dukes for a long time. Dukes afterward varied in power, but the Bourbons were strong enough they became the dominent power in France after some times, so there's that.

In 1000 A.D. the French King was Robert the second who had small holdings as crown lands, he had thus much less income than all of the dukes, he inherited the duchy of Burgundy later in his reign (but his heir would give it to his brother) and managed to gain some counties, notably the county of Paris, he had authority upon his peers but most likely was too weak to keep them in line. He famously had trouble to claim the duchy of Burgundy and had to resort to a Church Ruling to inherit it, since he didn't manage to conquer it. He managed to stay the king by allying a lot with his vassals, which he treated more as equals. He's maybe one of the Capetian kings we know the less about, his wikipedia page should give you an headstart to find whatever else you wish.

Sources : List of dukedoms in France , Peers of France , Robert II (the French link has a lot more details)