England's relationship with continental Europe during the Middle Ages was a complex one.

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The Angevin Empire

As u/Sword7770 said, England and France were deeply intertwined when William the Conqueror gained the Kingdom of England in 1066; he was a vassal of the king of France because of his Duchy of Normandy. This situation radically changed, and quickly spiralled into continual conflict, when Henry II became King of England in 1154. Because of his marriage to Eleanor of Aquitaine, one of the most interesting people of the Middle Ages, he became feudal lord a vast swathe of French land which immediately made him more powerful than his nominal liege lord, the King of France. Indeed, at this point it becomes, in my opinion, something of a misnomer to refer to the 'Kingdom of England' when discussing the Plantagenets; the English crown, in the same sense as the Crown of Aragon is used, would be better in my opinion, and this is something I will return to. The lands held by the English crown are now referred to as the Angevin Empire, after the region from which Henry's father, Geoffrey Plantagenet, was born.

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In anycase, Henry II and his immediate successor, Richard I (the 'Lionheart') were both involved in almost continual warfare with the Kings of France and their proxies, such as the Counts of Boulogne or Flanders, because of the huge extent of their dominions in France. Indeed, England became something of a military camp, which exported money and men to the continent. Richard did take part in the Third Crusade and he actually conquered Cyprus. He chose not to keep it however, first selling it to the Knights Templar before eventually granting it to Hugh of Lusignan, one of his vassals, after recognising just how overstretched his realm was. This is an important point. Henry II spent much of his reign in the saddle, constantly putting down threats whether they were in Ireland, Scotland, Wales or France. Richard I was destined to do the same, and any further strain on the resources the English Crown possessed could prove fatal to their richest dominions, which lay in France and England itself.

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The majority of the French lands held by the English crown were lost by John I, known to posterity as Lackland, and the attempts by both Henry III and Edward I to regain them proved futile.

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The 100 Years War

This brings us to the beginning of the 100 years war. Edward I's grandson, Edward III, was the son of a French princess, Isabella. The death of Charles IV in 1328 lead to the ascension of Philip VI, due to the operation of Salic law. Edward refused to do sovereignty for the portion of France he still held in right of the French King, Gascony, and Philip therefore declared the fief to be vacant, legally dispossessing the English king of the region. War would begin in 1337 in what is referred to as the Edwardian phase of the 100 years war, but it is unclear whether Edward really was pressing his legitimate dynastic claim to the French throne, or if he wished to simply hold the lands he conquered in France in his own right, which would mean the French no longer had any legal rights to them and he would no longer be required to pay homage for them. The treaty of Bretingy, signed in 1360, saw Edward renounce his claim in return for his duchy of Aquitaine being increased in size, for instance.

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Henry V, who began his own campaign in France after a long period of English losses, did press his own claim to be King with far greater consistency than Edward, and was able to have his children recognised as the legitimate heirs by the Treaty of Troyes, signed in 1420. His success, as well as the previous power of the Angevins, shows why he would continue to want to be involved on the mainland. It was hugely prestigious, and it brought great wealth back to England. Furthermore, the noblemen were in a great position if they contributed to his campaigns to win yet more land abroad; this was one of the problems that led to John I's failed campaign to retake his French lands, since the noblemen simply did not have any impetuous to commit themselves to it.

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Military Tech

I think a quick word on this should be said. I am by no means the most qualified on the topic, but the English armies of the Middle Ages were some of the most technologically advanced in Europe. They were wealthy enough to field knights and well armed horsemen, although they did prefer to fight on foot. Furthermore, the use of billmen and mercenaries effectively rounded out English forces, although men at arms were more commonplace by Henry V's reign (from what i have read).

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Of course, the decisive factor was the longbow and its users. Whilst they had to be properly protected & utilised- as defeats such as Patay in 1429 illustrate- they were devastating when they were used correctly, as Agincourt, Crecy and Poiters show. The English were by no means technologically backward.

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The English Crown

Whilst it is easy to view the English during this period as pouring resources only on France, this was by no means the case. A review of the titles held by John , for example, brings up examples such as King of England, Lord of Ireland, Duke of Normandy and Aquitaine. This is a huge swathe of land (see attached link) and also ignores the huge influence the English kings held over the Kingdom of Scots too. The Hiberno-Norman aristocracy was firmly established by Henry II's period of exile on the island following the murder of Thomas Beckett, and Edward I's attempts to bring Scotland far more firmly within the aegis of the English crown should be remembered too. In all seriousness, the English crown was far more varied than just its holdings in France, although they formed a huge part of them.

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Expansion elsewhere

Part of your question was why the English crown did not attempt to expand elsewhere. As i showed with Cyprus and Richard I, expansion into the Middle East was not realistically feasible. Scandinavia was also not feasible- whilst the realm of Knut I had effectively, been a North Sea Empire, this would simply have taxed English naval resources far too much at a time when they had to deal repeatedly with both the French and Castilian navies.

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Ireland and Scotland, as i discussed above, were both firmly within the English crown's aegis, although the level of control fluctuated wildly. Whilst I am not hugely familiar with the Irish politics of the time, I am of the Scottish ones. Cross-border holding prior to 1296 was hugely common. Whilst they Alexander III of Scotland had managed to move the Scots away from total English domination, he was still denied a full coronation due to the agitation of the Archbishop of York at the Papal Curia, which claimed Scotland to be a part of England. It effectively was; whilst only Malcolm IV did feudal service on behalf of his liege lord, serving at the siege of Toulouse in 1157, the imposition of legal English lordship, although ambiguous, was recognised throughout Europe.

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Finally, as you note, the Americas had not been discovered for the vast majority of this reply. Any attempt at large scale colonisation would probably be doomed to fail, as the difficulties at Jamestown and elsewhere illustrate.

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Hopefully this helps answer your question.

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Sources:

The Plantagenets, by Dan Jones

The Hollow Crown, by Dan Jones

The Three Edwards: War and State in England 1272-1377, by Michael Prestwitch

Edward I, by Michael Prestwitch