In XVIth (and early XVIIth century) France, clergy was a generally good career option if you were a smart peasant child, even of poor background, with some ambition and that your village's clergyman noticed as "one of the smart kids".

A good example is the biography of Jacques Amyot, a famous clergyman and humanist writer of the XVIth century, born in Melun in 1513 (so possibly not the son of a farmer but maybe a poor craftsman^1 ^2 (as Melun would have been a relatively decently sized city in that era). In any case, he was from obscure background.

Noticed by the priest of his parish, he went up to Paris to follow (theology) courses in the Sorbonne, tutoring richer students to make a living. Aged 19 he graduated, then followed up with a doctorate in civil law in Bourges (then a relatively important city of the kingdom : we are around a century after the peak of fame of the city under the dukes of Berry and Jacques Coeur), under a famous italian professor. Through various tutoring jobs, in particular in ancient greek where he seems to have been gifted quite early, he was awarded through court connections a tenure job in the Bourges university in Greek and Latin. [In the mid-1540s, Bourges would have been all the more important as it was close to the Loire valley where the court famously stayed between the different royal residences]. A famous translation of a work by Heliodore saw him granted the benefits of an abbey in 1547. He was then named preceptor to the Fils de France (children of Henry IInd) : François IX named him Grand Aumonier de France, then Henry IIIrd made him a commander of the order of the Holy spirit. By that time he was a relatively important figure in court. He was then named bishop of Auxerre (relatively important city in Burgundy) in 1570, and a superior of the Hospital of the Quinze-Vingts (Hospital for the Blind in current-day 12th district of Paris, which still exists and still specializes in ophthalmology).

He is extremely famous to this day for his ability in ancient greek and remains the reference translation of Plutarch (Parallel Lives in particular) in France (still extensively read and published) : his easily understandable and straightforward translating style is a matter of example in greek version classes. Actually, his translation of the Vies Parallèles is rumored to have inspired the Roman plays by Shakespeare (in the Thomas North retranslation to English^3). He also translated 7 books of Diodore of Sicily. He is remembered as an acquaintance of Montaigne (and for having been respected as a fellow scholar by Montaigne, which says a lot !^4).

Another very famous example from the early XVIIth century is the cardinal Mazarin, Richelieu's successor as main Minister of State (the closest thing to a Prime Minister French Ancien Régime had) and a major figure of the first half of French XVIIth century. While not descended from peasants but from a relatively poor Italian merchant family, he came, through political shrewdness and astute scheming (but not as high a level of education as Amyot who was one of the major scholars of his time) to be a Prince of the Church (cardinal) while never taking full vows of a priest, a major figure of the French kingdom and the largest fortune of his time (through extensive embezzlement facilitated by his young advisors Fouquet and Colbert, all from non-noble backgrounds, and who would both become ministers of Louis XIV).

Also, regarding the idea that clergy is a good way to go up the social ladder, we all remember the Rouge et le Noir by Stendhal : while it happens in the early XIXth century in Restauration France, the story would have fitted correctly in earlier centuries.

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^1 : This is the generally accepted opinion derived from traces in the city archives of Melun : see for example the detailed information on the website of the Archives départementales de Seine-et-Marne here.

^2 : « Vie de Jacques Amyot, tirée des mémoires concernant l’histoire civile et ecclésiastique d’Auxerre », abbé Lebeuf, Melun, 1848

^3 : Chisholm, Hugh, ed. (1911). North, Sir Thomas. Encyclopædia Britannica. 19 (11th ed.).

^4 : See the Essais, II, 4