In his PhD Thesis, "Man, Society, And Knowledge In The Islamist Discourse Of Sayyid Qutb" by Ahmed Bouzid (Virginia Polytechnic Institute and State University, April 1998), Bouzid states the following (p.70-71):

A sustained target of his criticism in this "modern jaahiliyyah", and, in Qutb's eyes, one of its most articulate and intelligent spokesperson, is the French scientist and philosopher, Alexis Carrel (1873-1944).

He also says (p.219):

To make the same point, Qutb often quotes, and at great length, the French scientist Alexis Carrel

And also (p.240):

For example, the author Qutb quotes most extensively is the French Alexis Carrel, with whose ideas and observations Qutb seems to have been greatly impressed.

L. Carl Brown, writes in "Islam and Politics Past and Present: A Bibliographical Essay", referencing Youssef M. Choueiri,

[Youssef] Choueiri also explicates one of those seemingly minor points that actually is very revealing (pp. 142-49). This is the extent to which Sayyid Qutb was influenced by Alexis Carrel (1873-1944). Carrel, a medical doctor, received the Nobel Prize in 1912, but his importance here was his later book, Man, the Unknown(a best-seller in the 1930s and 1940s) and his easily fitting as an official in the government of Vichy France. Carrel put himself forward as a social philosopher (if not, indeed, a prophet) deploring the presumed dehumanizing impact of modern Western materialism (especially capitalism). A social Darwinist elitist, he went all the way into advocating eugenics and euthanasia to breed the best and weed out the unfit. Qutb, Choueri argues, adapted Carrel's ideas (not, in fairness, eugenics and euthanasia) to come up with "a Third World version of fascism." Choueiri shrewdly suggests that what Carrel called modern Western "barbarism" could be transposed into Qutb's jahiliyya. An excellent insight, which also demonstrates that even Islamists most intent on rejecting the "other" in favor of a postulated cultural authenticity often rely on theories and ideologies advanced by outsiders.

Ibrahim Abu Rabi' (a professor of Islamic Studies at Hartford Seminary) also said, in an interview that took place with Religioscope on 8th November 2001, when asked, "Qutb was also an avid reader as you observed. It seems however that you think the influence of other authors was not as strong as a number of scholars claim. You consider that the main influences upon him were his reading of the Quran and the historic situation in Egypt", he replied:

Yes. After the 1940s. But before that he had been influenced by a great number of authors. Even after the 1940s, this French medical doctor, Alexis Carrel, influenced him.

Qutb's analysis of the Muslim world drew out of the influence of Carrel's analysis of Western society, and this determined the nature of the ideology of Sayyid Qutb, later in his life. The themes of barbarism (i.e. Jaahiliyyah) are touched upon often by Carrel. Alexis Carrel writes (Man, the Unknown, p. 27 and 28):

We are unhappy. We degenerate morally and mentally. The groups and the nations in which industrial civilisation has attained its highest development are precisely those which are becoming weaker, and whose return to barbarism is the most rapid.

Alexis Carrel also writes (Reflections On Life, p.103):

It is to these vices that the great nations partly owe their decline. In the years before the war they were the greatest consumers of alcoholic drink in the world. Alcoholism, nicotine poisoning, sexual excesses, the drug habit, mental dissipation and low morals all constitute extremely dangerous breaches of the law of self-preservation. These vices weaken the individual and mark him with a special stamp. The young Frenchman of the defeat: rude, slovenly, unshaven, slouching about with his hands in his pockets and a cigarette in the corner of his mouth, was all too representative of the anemic barbarism on which the France of those years prided herself.

Alexis Carrel also says (Reflections On Life, p.195):

Civilization is first and foremost a discipline; a discipline which is physiological, moral and scientific. barbarism, on the contrary, is essentially undisciplined. But whereas primitive barbarism was subject to the harsh authority of nature, our anemic modern barbarism is completely unrestrained.

Qutb has many statements that are similar in nature, and his reaction to Western influence in the Muslim lands takes a similar course. Sayyid Qutb wrote (Milestones p.21):

Today we are in jaahiliyyah (barbarism), like that which was prevalent at the dawn of Islaam, in fact more oppressive (i.e. severe). Everything around us is jaahiliyyah...

Being ignorant, and speaking about Islam from his opinion and intellect, and being influenced by his own experiences, he continued down the line of ignorance and excess, by making takfir of all contemporary Muslim societies, based upon this "barbarism". Sayyid Qutb wrote (Milestones p.103):

Entering into the realm of the Society of Ignorance (al-Mujtama' al-Jaahiliyy) are all those societies which claim that they are Muslim societies...

And also (Milestones p.103):

The position of Islaam towards all these societies of jaahiliyyah (ignorance and barbarism) can be defined in a single expression: It rejects any acknowledgement of the Islaam of all of these societies.

And also (In the Shade of the Qur'an, adh-Dhilaal 4/2009):

Indeed this Jaahili Society that we live in is not a Muslim Society.

On 31st July 2007, the German paper, in its online version, Zeit Online published an article by a historian called Rudolph Walther. The article is called "The Strange Teachings of Doctor Carrel: How a French Catholic doctor became a spiritual forefather of the radical Islamists."

The following are excerpts from the article. The translations are from another source on the web:

The superficial commonalities between Carrel and Qutb are plain: we meet the medical man's elite in a "scientific monastery" as Qutb's "avant garde," and the Carrel's "biological classes" are Qutb's "belief classes." Whether "civilization" (Carrel) or "barbarism" (Qutb) -- neither are "worthy of us," because they contradict "our true nature" (Carrel) or Qutb's "good, healthy nature." Both are quite in agreement in their goal to reconcile knowledge and belief...

The decisive affinities lie deeper, though. Qutb cites no author aside from the Koran as often and as extensively as Carrel. What fascinated Qutb about Carrel was, as Islamic Studies scholar Ibrahim M. Abu-Rabi wrote in his 1996 book "Intellectual Origins of Islamic Resurgence," first of all his view of humanity "which he relies on more than the Koran." Second, Qutb follows Carrel's method. The pious doctor complains that "man, this whole," this unique, complex being, is being subdivided and torn apart by social reality and science... The exclusive concentration on the material nature of man had the effect of repressing his spiritual side...

Qutb follows Carrel in making "human nature" the condition and measure of all thought and action. Because "human nature" is simultaneously posited as God-given, both immunize "human nature" against criticism, because God answers queries as little as "nature" does objections. The core of Qutb's supposed Middle Eastern Islamism is formed by a naturalistic logical error that is deeply rooted in European philosophy... Carrel writes: "The goal of life is to follow the laws of life. We decipher these laws from our bodies and our souls, not from philosophical systems and concepts." Thus ethical norms ("laws of life") are derived directly from biological facts and psychological diagnoses. Translated to Qutb's language, human freedom and thus a free, varied society are not possible, only obedience to the law of God...

What Qutb calls "the Islamic method," the integration of education, ethics, economics and politics to a unified system of "divine uniqueness," matches Carrel's "unification of all capabilities and their coordination to a single belief," the "super-science" in every detail...

The roots of Qutb's concept of "jaahiliyyah" lies in the influence of Carrel's parallel concept of "barbarism". Alexis Carrel was a Christian and a social philosopher who wrote on the subject of the decline in the socials and morals of Christian society and offered solutions to the prevailing trends he saw. Qutb concurred with many of Carrel's ideas, observations and reflections.

This heavy exposure to Carrel, pre-1940s, would set the stage for Qutb's later ideological development, when he would visit the United States for a Masters degree in education, as then Minister of Education for the Egyptian government, where he would witness for himself the nature of American permissive society. This pushed him in the direction of developing his theme of "jaahiliyyah". The influence of the revolutionary philosophy of Mawdudi would also play a role in the evolution of Qutb's methodology. However, the point to note here is that the origins of Qutb's later doctrines lie in his earlier pre-Islamist days, before the late 1940s.