This is a difficult question to answer in a straightforward way because not only were the philosophers of both the Greeks and the French unique in comparison to each other, but they were also internally variable. Furthermore, the views of both Greek and French philosophy change depending on what time period you are considering. To simplify this question, we can focus on some of the most famous philosophers of arguably the most intellectually influential time periods of each respective civilization. For the Greeks, this would be the Classical period from roughly 480–323 BCE. For the French, we may consider some of the philosophy of the Enlightenment, which took place primarily in the eighteenth century throughout all of Europe.

Two of the most famous Greek philosophers, and perhaps of all time, were Plato and Socrates. Because all of our information on Socrates was passed down to us by what his student Plato wrote (as Socrates never wrote anything himself), it is difficult to distinguish between the ideas of these two men, as much of Plato’s writing takes the form of dialogue in which Socrates is the main character.

Essentially, both Plato and Socrates believed in the discovery of absolute Truth, which they understood as the “Forms” or “Ideas.” The “Idea” of any subject, such as love, justice, courage, beauty, and so on, was unchangeable, and consisted of the most perfect understanding of it, free from any logical inconsistency. Both men believed that knowledge obtained through sense perception was fickle and subject to constant change—a tree which is perceived to be beautiful by one man may be seen as not beautiful by another, so how can the same tree be both beautiful and not so? Plato and Socrates argued that in order to move beyond this relative, imperfect understanding of concepts, it was necessary to engage in a dialectic, or a logical, self-reflective questioning of assumed knowledge, until one reached a point at which they could no longer contradict their internally held presuppositions.

This kind of philosophy privileged the mind over the senses and claimed that objects in the external world, as well as the concepts associated with them, could only be perfectly understood at the level of the mind. This philosophy was in some ways a response to other Greek intellectual discussions taking place at the time that were concerned with the fundamental essence of nature. For example, Democritus, most famous of the atomists, supposed that all matter was composed of indivisible units that he called atomos, beyond which they could no longer be broken down. Other philosophers of the period, including Aristotle and Xenophon, were similarly interested in understanding the truest forms of nature.

During the Enlightenment, French philosophy, as well as that in most other parts of Europe, was highly inspired by the ideas of modernity and progress. It was an important milestone in Western thinking because the Enlightenment, which directly succeeded the European Scientific Revolution, seriously challenged the centrality of God as a causal factor in human history. However, just as the Judeo-Christian worldview argued for the teleological progress of humanity, from the first creation to the second coming of Jesus Christ, the modern worldview of the European Enlightenment also adhered to the principle of teleological progressivism.

Instead of God, philosophers trusted in the human attributes of rationalism, empirical thinking, and sound organization to move civilization along a positive path of development. This is important to keep in mind because much of Enlightenment philosophy still adhered to a monolithic, teleological way of thinking, and any social composition, worldview, or cultural phenomena that deviated from this teleology was deemed barbaric and inferior.

The writings of the French philosophers reflected this intellectual trend. Montesquieu, for example, in his famous The Spirit of the Laws, posited that different climates predetermined the types of governments that different parts of the world would enjoy. Sub-Saharan Africa, lying as it was close to the equator and of interminable heat, was destined to be ruled by savages with little to no political consciousness. The Mediterranean nations, however, lying further north in the temperate European climates, were more docile and thus open to proper forms of governance. Montesquieu argued that the best kind of government (which, of course, France exhibited) was the limited monarchy, in which a monarch held powers that an intermediary body of advisors could check. It is important to note here that Montesquieu’s kind of thinking, which was shared by most literate men in France and elsewhere, in one form or another, directly justified European colonialism and slavery by relegating non-European peoples like the African tribesman to an inferior place on a global hierarchy of civilization.

Voltaire, perhaps the most famous French philosopher of all time, similarly believed in the merits of enlightened monarchy over all other forms of government, and he engaged in a lengthy and gushing correspondence with the Russian monarch Catherine II, in which he endlessly praised the superiority of Russian governance. Other French thinkers at the time, influenced as they were by the belief in the perfectibility of civilization, attempted to collect all available human knowledge in one place so that it might be put to the best possible use in creating the most ideal society imaginable. Denis Diderot and Jean le Rond D’Alembert famously compiled their Encyclopedia, the most famous of such epistemological compendiums, and the French minister of finance during the reign of Louis XIV, Jean-Baptiste Colbert, was infamous for the massive imperial libraries that he constructed.

This is a very good question. However, as the question stand, it is almost unanswerable, because neither Greek nor French philosophy is monolithic. There is so much variability among philosophers!; no two agree! Moreover, there were many of them.  So, even generalizations will be imprecise to say the least. In light of this, let me just mention a few points that will help you get into this topic. 

The two greatest philosophers in the Greek world were Plato and Aristotle. They both believed in what is known as the forms. The forms  can be thought of as universal truths. Plato believed that the immortal soul could know these forms. Aristotle believed that these forms could be known more fully through investigation. Hence, Greek philosophy had knowable universals. 

When we come to the French, many of their philosophers (post-modern era) have done away with the idea of knowable universals. They have moved beyond things like structuralism. Instead, they say that all knowledge is socially constructed and therefore relative. Some of the famous names in this camp are: Foucault, Derrida, and Deleuze.