If the juice of the grape was young, meaning that it was just from the vine and had not set for any length of time, it would have been lightly fermented. It would have been a drink with little, but some, alcohol. If, on the other hand, it would have been allowed to set and ferment for a longer period of time, it would have been more potent (in alcoholic content).
The wine, in those days, had an amount of alcohloic content. Some less, some more. The people of that time knew this, and the beverages were considered a gift, and they cherished the taste and the experience of the wine. They considered it a gift from God and it was coveted as riches for the common man.
Note: all wine has a certain amount of alcohol, that is a biochemical fact. How you treat that wine, preserve it, let it brew, etc. is the factor in the alcoholic content of the wine.
Try this: pick grapes, smash the juice out of those grapes, let the juice and the fruit set of one day. Then drain off only the juice and let it set for another 4 days. Then drink it. You will get a buzz. Why? The sugar and juice are in the grape, the yeast (in the form of yeast spores) grow on the skin of the grape. God's perfect booze! All you have to do is follow the instructions. "Pick, stomp, wait, contain, and wait again"! Direct to you from that little old wine maker....God!
I've brewed many a batch of Ale and a few batches of wine (nothing drinkable by my standards).
At room temperature most fermentation will be done in the first week. No skin could hold the CO2 produced during this week (it's many times the volume of the wine). After this initial fermentation the wine was transfered into skins. Small amounts of CO2 were still produced which would burst the old skins (much later a controlled version of this second fermentation would produce carbonation).
Jesus not only drank real wine, his first recorded miraculous act was turning water into wine. Good marketing for the religion.
He would never touch Buttweiser though.