First of all, it's important to note that, because most people were illiterate in this distant period, we have relatively little information on ordinary soldiers. As such, a lot of what historians 'know' is what they've worked out, not what a written source has explicitly told them. Nearly all English soldiers that fought in the Hundred Years War were volunteers. They were raised through a system of indenture, where a king or prominent nobleman provided a lesser aristocrat or captain with much of the funds necessary to recruit and maintain troops. Nevertheless, soldiers usually provided their own equipment. All soldiers (even dukes) received a regular wage, though this depended on rank and equipment. Noblemen and knights got paid the most, then men-at-arms, then mounted archers, then foot archers. Even the foot archer's wage, however, was quite good for the time. The greater enticement of war though was often the booty that might be taken on campaign. Looting was carefully regulated, in that the general and the captain each took a set share of what the common soldier looted.

Because the soldiers were English, we wouldn't describe them as mercenaries, though they weren't levies either. They were sort of semi-professional soldiers. The English did have permanent garrisons in France (especially in the Lancastrian phase), but most soldiers would have served in a particular campaign, before returning to civilian life. They might 'sign on' again in another campaign, so as the wars went on there would have been plenty of experienced soldiers.

In medieval England everyone, even the upper nobility, was theoretically a tenant of someone else. Most people were peasants, and most peasants were, by the mid-fourteenth century, free tenants of some sort, paying rents to the landowner. There were some serfs still but the labour obligations they owed to their lords made it more difficult for them to go to war. The men who went to war would often have been those who were surplus to agricultural labour requirements; second sons and the like. As for whether they'd have been married or unmarried is a very interesting question. Ordinary people tended to marry in their late teens or early twenties, but usually didn't wed until they had the wealth to set up their own household, in contrast to Southern Europe, where people usually married earlier and stayed with their parents. As such, some men would have gone to war to accumulate the wealth needed to set up their own household and marry. As for whether the 'average' soldier was the son of a soldier, that's unclear. Obviously this would have become more common as the wars went on. Sons of soldiers would have seen the wealth that soldiering could bring. More practically, old soldiers could have passed their weapons and armour down to their sons.

C.T. Allmand's Society at War: The Experience of England and France During the Hundred Years War is a great little sourcebook for this. I've also made use of Jonathan Sumption's multiple volume The Hundred Years War, which contains a lot of social history even though it's primarily a military and political narrative.

I asked a somewhat similar question that has answers from /u/Knight117 and /u/MI13 that might interest you.