If Vedas were to be "heard" in the medieval era by the sages, I am sure they might have composed it in Awadhi or some other common language, as even Tulsidas composed.
As C. V. Vaidya says in the History of Sanskrit Literature, Vedic Sanskrit is simply the language spoken by the common people during the Vedic period.
Macdonell divides the history of Sanskrit literature into two periods, the Vedic period and the Sanskrit period. But it is more proper to divide the history into three periods, the Śruti period, the Smṛti period and the Bhāṣya period, as we propose to call them. The language of the Vedic literature can be given no other name than Sanskrit, the Indo-Aryans brought with them into the Panjab a branch of the language of the ancient Aryan people which may properly be called, by distinction, Sanskrit. This name no doubt arose later when the Prakrits came into being, by way of opposition, meaning the language of the refined people, as opposed to Prakrit, the language of the common people. But that name has to be carried back to the Vedic times. If Sanskrit is a name which is to be confined to the language of Patañjali's days, Vedic literature cannot come within the range of a history of Sanskrit literature. We may call the Vedic language Vedic Sanskrit, the language of the days of Pāṇini post-Vedic Sanskrit, the language of the days of Patañjali classical Sanskrit and the language of the days of Śaṅkarācārya and after modern Sanskrit. The language is the same throughout this length of time, though it has different aspects in these four, rather three, periods, just as English has been divided into old English, Elizabethan English, and modern English. It is needless to state that the identity of a language continues so long as its grammar remains practically the same.
The Vedic people actually spoke this Sanskrit language in the form it then had and the Vedic singers did not use an artificial language for their poetry as is sometimes supposed. There was, in the beginning, no Śūdra caste, the Aryans being homogeneous; the cultivators, the warriors and the priests, being of the same Aryan race, were of the same mental and physical capacities. There was then a slight difference between the spoken language of the common people and that of the higher class people, such as exists in every country and at every time. The language of the Vedic common people must, however, still be called Vedic Sanskrit; and it is interesting to find that when the Aryans migrated to the Deccan, they carried words of this Vedic Sanskrit, some of which still survive in the language of the common people of the Deccan. The pronoun tyo, used by common people, instead of to used by higher classes in Maharashtra, is a survival of the tyas of Vedic times. In short Vedic Sanskrit was a spoken language as well as post-Vedic Sanskrit of the days of Pāṇini. The language had changed visibly by this time; but it was still the same language and Pāṇini gives no separate grammar for Vedic Sanskrit, but simply marks certain peculiarities of the language as used in the hymns. He always makes the simple distinction bhāshāyam and chhandasi where there are differences. The word bhāshāyam used by Pāṇini clearly proves that it was a spoken language of which he wrote the grammar and that the name Sanskrit had not yet arisen, nor of course, Prakrit.
For these reasons, therefore, it would be appropriate to divide the history of Sanskrit literature into three periods; viz., the Vedic and post-Vedic period (c. 4500 B. C. to 800 B. C.) to be called the Śruti period, the classical period (c. 800 B. C. to 800 A. D.) to be called the Smṛti period and the modern period (c. 800 to 1500 A. D.) to be called the Bhāṣya period. In the first period, Sanskrit was spoken by all people who were chiefly of the Aryan race; in the second, it was spoken by the high class males while their women and lower classes spoke the ancient Prakrits which were only softened Sanskrit; and in the third period Sanskrit was dead as a spoken language. Naturally the literatures of the three periods differ in language — easy and simple in the first, polished and refined in the second and artificial and pedantic in the third. Then again in the first period, literature is chiefly religious and philosophical and at once became sacred. In the second period literature is highly thoughtful and has become quasi-sacred or authoritative, where not religious, and in the third period literature becomes scholastic though usually full of powerful reasoning and forceful expression.
Rig veda 1.164.39 says as follows:
रचो अक्षरे परमे वयोमन यस्मिन देवा अधि विश्वे निषेदुः | यस्तन न वेद किं रचा करिष्यति य इत तद विदुस्त इमे समासते ||
ṛco akṣare parame vyoman yasmin devā adhi viśve niṣeduḥ | yastan na veda kiṃ ṛcā kariṣyati ya it tad vidusta ime samāsate ||
The vedas rest in the imperishable syllable - OM (ॐ) - in the Supreme ether (of the heart). Those who do not know that, what can they do with the veda? Those, who know that are gathered here
Aksara - अक्षर means imperishable. That which is imperishable is DIVINE. It was first made known to mankind through Sanskrit language. So Sanskrit is DIVINE.
While quoting the statement from Abrahamic Text "In the beginning was the Word and the Word was with God ", Swami Vivekananda said that the Word is the Vedas, and Sanskrit is the language of God. God spoke once. He spoke in Sanskrit.