I'm wondering whether an average Englishman would know that the Venetians and Ottomans were at peace again after the battle of Lepanto, or indeed know if England was on cordial relations with Denmark or Spain.
The international arena of the 16th and 17th centuries seems to change so much, how up to date would the average Englishman have been?
Well, the "average" English person would be an illiterate farmer; if they had much idea about foreign affairs, the knowledge would come from a literate person within the village reading a pamphlet or tract covering the event. If the conflict had religious import (and many did), they might also hear about it at church services. The extent to which an English person would know or care about such things would also depend upon their location—to overgeneralize, the closer to London, the more likely they were to be engaged.
For the late 16th and 17th centuries particularly, one's religion was also a determining factor in how "keyed in" one was to foreign affairs. Puritans, who were already more likely to be of a middling class and at least somewhat educated, were often keenly interested in formal affairs as they felt a strong tie to other Reformed Christians across Europe; an increasing number also felt that an apocalypse of some sort was inevitable, and looked to foreign affairs for portents of the coming end times. Catholics might look towards a time when England might return to the fold of orthodoxy, and would be eager for news that Catholicism was faring well against Protestantism on the Continent.
An anecdote to illustrate how English citizens understood England's relationships with foreign powers: when Prince Charles Stuart returned unsuccessfully from his ill-advised and ill-executed attempt to win the hand of the Catholic Spanish Infanta in marriage, reports indicate that spontaneous celebrations of the Prince's "safe return" (by which they meant return without news of a Spanish Match) broke out where ever the news spread. Protestants throughout England, not without reason it turns out, were concerned that a Catholic Queen Consort would influence Charles towards Catholicism and throw the English Church into upheaval yet again. Similarly, the marriage of Charles' sister, Elizabeth Stuart, to the Calvinist Count Palatine Frederick V was seen as a moment for sincere celebration.
Sources:
Crawford Gibbon, The Puritan Millennium.
Thomas Cogswell, The Blessed Revolution.