I presume you have Ancient Greek texts in mind so I'll speak about them - Classical Latin texts, on the other hand, such as the works of Sallust, Cicero, Caesar, Lucan, Virgil and Ovid had already been recovered and copiously copied by the 9th century, and were standard fare in the medieval cathedral school curriculum for the the study of Latin grammar and rhetoric from the 11th century on. Exemplary of this is a text like William of Poitiers' "The Deeds of William, Duke of Normans", his panegyrical biography of William the Conqueror that takes the Republican Roman historian Sallust as the literary model, compares the Hastings campaign of 1066 to Caesar's invasion of Britain in 55 BC and is littered with references to the other four authors I mentioned above. The only sense in which the humanists from Petrarch onwards really brought about a renaissance regarding classical Latin texts was the revival of "Golden Latin" (the form and style of written Latin used by Roman authors in the two centuries on either side of the birth of Christ - the Latin of Cicero, Virgil and Pliny) as opposed to the various forms of medieval Latin that had evolved over the centuries - humanists were big purists about language, as we'll see, and one can credit the renaissance for leading to the rise of philology as an academic discipline.

Greek, on the other hand, was a different matter. Knowledge of Greek was in decline in the Western Roman Empire after the crisis of the Third Century (235 - 284), prior to which the Roman civilian aristocracy had been practically bilingual (Latin translations of Greek authors were starting to become available from the 1st century BC, such as the abridged Latin version of the Iliad attributed to Publius Baebius Italicus, written around 70 BC which would be widely read in the Middle Ages and would be used by William of Poitiers as part of his panegyric to William the Conqueror, likening him to Agamemnon sailing to Troy when setting out from Ponthieu to invade England). For example, St Augustine, so far as his "Confessions" are to be believed, tells us that he received a pretty poor education in Greek during his schoolboy days in Roman Africa. After the death of Boethius in 525, who along with Cassiodorus and Gregory the Great was one of the last great senatorial aristocrats educated under the traditional system who had tried his best to create Greek textbooks prior to his execution due to suspected treason with the Eastern Roman Empire by Theodoric the Ostrogoth. Knowledge of Greek was not completely unheard of the early medieval West - Rome itself, in Venice and in the Southern Italy it was still studied, and there was a mini-renaissance in the study of Greek in Anglo-Saxon England as a result of the school at Canterbury founded by Theodore of Tarsus (602 - 690), a Greek archbishop of Canterbury, as the Venerable Bede makes known to us in his "Ecclesiastical History." Still, it wouldn't be until the 14th and 15th centuries that Greek secured itself a place on the Western European school and university curriculum, a development no doubt helped by Byzantine refugee scholars. No one forgot about the Ancient Greek authors, but many medieval intellectuals were content to read them in Latin translation (as with Homer's "Iliad") or to have their works paraphrased in Roman authors i.e. Herodotus' stories of Persian kings Cyrus the Great and Xerxes being recounted in Valerius Maximus' "Memorable sayings and doings" (written early in the 1st century AD and very popular in 14th century France after the knight hospitaller, Simon de Hesdin, translated it into French). A lot of Greek philosophical, mathematical and scientific works made their way into Western Europe in the 12th and 13th centuries via Islamic Spain, where they were actively sought out by scholars like Gerard of Cremona (died 1187) and Herman the German (died 1272), who would go over there to learn Arabic so that they could then translate those works back into Latin, enabling Western European scholars like Pierre Abelard, Albertus Magnus and Thomas Aquinas to revive Aristotelian logic, science and metaphysics. The humanists were different in this regard, as they weren't contented with reading the Greek authors in the paraphrases of Roman authors or their original works in Latin translations, they wanted to go properly ad fontes and read the originals in the original language - this was the impetus behind the study of the New Testament in the original Koine Greek in the late 15th century, which would help lead to the Reformation. In addition to that, you had Byzantine scholars bringing over the Greek literary texts that had not been studied much in the medieval west (the poems, plays and histories, as opposed to the philosophical and scientific works that had been widely studied from the 12th century) and so the two naturally combined together. I hope I've done my best at explaining this.