There is a region for which Bloch's, Ganshof's, and Duby's theories work: West Frankia.

In post-Carolingian West Francia in particular, royal power diminished. Nobles developed local powerbases around particular regions. These nobles ranged from dukes to lower-ranking noble warriors (who eventually became known as knights). These numerous small-scale lords built fortified residences (castles) to dominate their localities. This process is known as “encastellation". These local nobles came to control:

Local law and justice
Violence
Raising troops
Collection of surplus resources

For example, Duke William of Aquitaine was largely able to govern his territory without too much in-put from a king. He raised armies and even had coins minted in his own name. And you have already seen how by 911 Rollo had carved out Normandy for a dukedom.

Image above: coin of Richard I, duke of Normandy; one such cion is now in the Fitzwilliam Museum in Cambridge

Lesser nobles answered only nominally to counts and dukes. Meanwhile, counts and dukes paid little attention to king. The court culture that had hosted the Carolingian Renaissance diminished. Meanwhile, local religious leaders and eventually nobles tried to regulate law and order in the absence of a strong central power. This led to treaties known as the Peace of God and the Truce of God. These agreements tried to limit violence to a few days of the week and to establish protected categories who could not be attacked. Take, for example, this Peace of God treaty from the Synod of Charroux (in what is now central France) in 989.

Following the example of my predecessors, I, Gunbald, archbishop of Bordeaux, called together the bishops of my diocese in a synod at Charroux.... and we, assembled there in the name of God, made the following decrees:

1 . Anathema against those who break into churches. If anyone breaks into or robs a church, he shall be anathema unless he makes satisfaction.

2. Anathema against those who rob the poor. If anyone robs a peasant or any other poor person of a sheep, ox, ass, cow, goat, or pig, he shall be anathema unless he makes satisfaction.

3. Anathema against those who injure clergymen. If anyone attacks, seizes, or beats a priest, deacon, or any other clergyman, who is not bearing arms (shield, sword, coat of mail, or helmet), but is going along peacefully or staying in the house, the sacrilegious person shall be excommunicated and cut off from the church, unless he makes satisfaction, or unless the bishop discovers that the clergyman brought it upon himself by his own fault.

From Oliver J. Thatcher, and Edgar Holmes McNeal (eds), A Source Book for Medieval History (New York: Scribners, 1905), p. 412.

Within 100 years, these sorts of documents had become more elaborate. See this Truce of God from the county of Flanders in 1063:

Drogo, bishop of Terouanne, and count Baldwin [of Hainault] have established this peace with the cooperation of the clergy and people of the land.

Dearest brothers in the Lord, these are the conditions which you must observe during the time of the peace which is commonly called the truce of God, and which begins with sunset on Wednesday and lasts until sunrise on Monday.

1. During those four days and five nights no man or woman shall assault, wound, or slay another, or attack, seize, or destroy a castle, burg, or villa, by craft or by violence.

2. If anyone violates this peace and disobeys these commands of ours, he shall be exiled for thirty years as a penance, and before he leaves the bishopric he shall make compensation for the injury which he committed. Otherwise he shall be excommunicated by the Lord God and excluded from all Christian fellowship.

3. All who associate with him in any way, who give him advice or aid, or hold converse with him, unless it be to advise him to do penance and to leave the bishopric, shall be under excommunication until they have made satisfaction.

4. If any violator of the peace shall fall sick and die before he completes his penance, no Christian shall visit him or move his body from the place where it lay, or receive any of his possessions.

5. In addition, brethren, you should observe the peace in regard to lands and animals and all things that can be possessed. If anyone takes from another an animal, a coin, or a garment, during the days of the truce, he shall be excommunicated unless he makes satisfaction. If he desires to make satisfaction for his crime he shall first restore the thing which he stole or its value in money, and shall do penance for seven years within the bishopric. If he should die before he makes satisfaction and completes his penance, his body shall not be buried or removed from the place where it lay, unless his family shall make satisfaction for him to the person whom he injured.

6. During the days of the peace, no one shall make a hostile expedition on horseback, except when summoned by the count; and all who go with the count shall take for their support only as much as is necessary for themselves and their horses.

7. All merchants and other men who pass through your territory from other lands shall have peace from you.

8. You shall also keep this peace every day of the week from the beginning of Advent to the octave of Epiphany and from the beginning of Lent to the octave of Easter, and from the feast of Rogations [the Monday before Ascension Day] to the octave of Pentecost.

9. We command all priests on feast days and Sundays to pray for all who keep the peace, and to curse all who violate it or support its violators.

10. If anyone has been accused of violating the peace and denies the charge, he shall take the communion and undergo the ordeal of hot iron. If he is found guilty, he shall do penance within the bishopric for seven years.

Translation from Oliver J. Thatcher, and Edgar Holmes McNeal (eds), A Source Book for Medieval History (New York: Scribners, 1905), pp. 417-418.