Invading England
Historically, the French were never able to invade England, although there were some serious attempts and such an enterprise was by no means impossible, simply quite difficult. English ships generally ruled the English Channel throughout the Hundred Years War. This control was not absolute, thus the game does provide for some chance of getting a French army over to England.
There are several ways for the French to get an Army to England, and not all of them are obvious:
1. Cross by sea from France with an Army raised in France. The obvious way. Advantages: requires no special PCs or timing. Disadvantages: unreliable and expensive (at best a low chance and a considerable expense for each attempt, successful or not). Historically, the French tried this several times, and always failed. It cost them hundreds of millions of ducats and, in effect, helped the English by draining the French treasury .
2. An English Traitor raises troops in England and transfers to a French General. This is done to hide the origin of the troops from the English who come upon the army in action.
Advantages: Gets an army without having to cross the channel. Gets Yeomen.
Disadvantages: You need a traitor. The French tried this in the original war, but were unable to convince any English nobles to stick their neck out that far. There is a limitation on the size of the army that can be raised this way (although by recruiting at London or another large population center quite a few men can be raised.) In the game the French have had mixed success getting English traitors. In several cases, the English "traitor" double crossed the French, kept the money and was in turn rewarded by the English king.
3. The Bruce (king of Scotland) does recruits an army in Scotland and transfers to a French General. This is very similar to 2 above except: 1) you do not get yeomen 2) you do not need an English traitor (hard to get someone to betray their own side, where the Bruce sees England generally as an enemy). 3) You are dependent on the Bruce (Only non-English position on the island of Britain.) The historical French tried this approach, with minor success. The Scots, unfortunately, are not eager to take on England as a major English military effort could conquer Scotland (which the English never did anyway, but they kept trying.)