THE SHORT ANSWER
Charles I did borrow money from abroad but it was never enough to meet his needs. The financial drain of the Thirty Years War on much of Europe, a muddled foreign policy, and a lack of both collateral and trust were the main reasons Charles I could not borrow enough abroad. Potential lenders were also reluctant to help the king due to the English Parliament's control of London and the navy.
THE MORE DETAILED ANSWER
That Charles’ needs were so great was partly due to his own extravagance but also to debts which he inherited from his father, James I. It should also be noted that
England was still the least taxed country in Europe, with no official
excise and no regular direct taxation.
Source: Pauline Gregg, ‘King Charles I’
Even so, the King’s financial situation at the start of his reign would have been alleviated to some extent had he had the trust of Parliament but
Buckingham’s disastrous attack on Cadiz seemed to confirm the worries
many MPs had had about his suitability as a leader. The king still
required money, loans secured on the crown jewels had funded the war,
but nothing costs more than a defeat
source: Martyn Bennett, ‘Oliver Cromwell’
Charles offset some of this through various domestic measures - for example, taxation by means of ship money from 1634 onwards - but none of his measures endeared him to his people.
In the early years of his reign (at least), Charles' favourite Buckingham's apparent attempt to seduce the French queen soured relations between England and France, even though Louis XIII and Charles were brothers-in-law.
Anglo-French relations had steadily deteriorated after the marriage of
Henrietta Maria to Charles in 1625. Louis and Richelieu were spoiling
for a fight with England, Richelieu because he had built a fleet to
rival the island state's seapower, Louis out of bad blood with
Buckingham for brazenly courting Queen Anne.
A. Lloyd Moote, ‘Louis XIII, the Just’
The involvement of so many European countries in the the Thirty Years War Limited Charles I's options for securing loans (red/pink = against emperor, black/grey = for emperor). Source: Wikipedia
Almost all of Charles’ reign overlapped with the Thirty Years War so some of the countries that the King might otherwise have been able to call upon were in no position to help. Europe was, in fact, costing Charles a considerable amount of money from the very beginning of his reign, including maintaining an army in support of the Protestant Union under the command of Count Mansfeld. Charles had committed himself to
the subsidies he had agreed to pay to the Protestant armies in Europe.
It remained to be seen whether he could meet these obligations:
£240,000 a year for Mansfeld and his men; £100,000 annually to help
maintain troops in the Low Countries; £360,000 for the armies of his
uncle the King of Denmark; £300,000 or more to equip and pay for the
fleet and army being prepared against Spain; £25,000 to protect
Preparing for war against Spain obviously ruled out that country, along with the Hapsburgs and their allies who were fighting the Protestant Union. Gregg adds that Charles
sought new ways of raising money, one of which entailed offering the
Crown jewels as security for a loan from Dutch financiers, but nowhere
did he find much support. Even from France, in spite of his marriage
treaty, he received little comfort.
From 1627 to 1629, England was at war with France so, even though his wife Henrietta-Maria was the sister of the French King Louis XIII, money from this source was obviously out of the question at this time. Later attempts to get French assistance fell on deaf ears despite the King’s personal intervention.
In the early years of his reign, Charles relied heavily on Philip Burlamachi, a financial intermediary. Gregg states:
Most of Charles's foreign transactions had gone through Philip
Burlamachi, whose credit stood pledged all over Europe to meet
Charles's needs. ...Charles was fortunate in having in his service one
of the great international financiers of the age whose word and whose
credit were unquestioned from the time he advanced money for the
little Duke's engines of war until he himself crashed in 1633.
Another potential source was the Pope but, despite the intervention of his Catholic wife Henrietta Maria, the Vatican would not consider assisting a Protestant king unless he converted to Catholicism (Gregg).
The Bishop’s Wars of 1639 and 1640, in which Charles came into conflict with the Scots, placed further demands on the King’s already fragile finances. With England no longer at war with Spain, Charles had
begun to look to Spain for financial or military assistance against
the Scots, canvassing schemes for obtaining 8,000 veterans from the
Army of Flanders in return for allowing Spain to recruit twice as many
fresh troops in Ireland, or for a substantial loan in return for a
marriage alliance. In the winter of 1639–40, as Charles prepared for a
second campaign against Scotland, reports of the successful conclusion
of the second scheme circulated widely in both England and Europe.41
The treaty ultimately failed, partly because Charles refused to meet
Spanish terms, but also because French and Dutch advances and the
revolt of the Catalans in June 1640 crippled Spain at the critical
Source: J. McElligott & D. L. Smith, 'Royalists and Royalism'
Charles, in allying himself with Spain, was unlikely to get anything from France as France and Spain were at war from 1635 -1659. Under the hugely influential Cardinals Richelieu and Mazarin, France was allying itself with Protestants fighting the Hapsburgs so one cannot assume that they would 'naturally' support Charles against Parliament. Further, the French government had little to spare (despite high taxes) and was itself looking for finance.
By 1640, Charles was so desperate that he
.....confiscated the gold and plate which had been deposited for
safekeeping in the Tower of London, destroying the reputation of the
mint as a safe place of custody. The treasure was returned only after
merchants and goldsmiths had agreed to lend the king £40,000 on the
security of the Customs Farm
Source: Charles B. Kindleberger, 'A Financial History of Western Europe'
As much of the treasure in the Tower belonged to Spain, this move could only have undermined Spanish trust in the English king. Nor did Charles's attempts to raise money in Amsterdam (by now the banking centre of Europe) meet with much success, despite the efforts of his wife Henrietta Maria. The bankers in Amsterdam, looking at the state of England's finances and undoubtedly well-aware that Charles had defaulted loans before, wanted collateral. The Queen had only the crown jewels to offer, and the bankers were reluctant to accept them for fear that they would later be reclaimed by the English parliament. Further, the Dutch were staunchly protestant and tended to favour the English Parliament.
Woodcut from the English Civil War showing the opposing sides. Both sides struggled to finance their armies but the Royalists' (on the left) financial woes were more pressing. Source: imgur
By the time the English Civil War started, it is evident Charles had burnt most of his potential foreign financial bridges, and the fact that Parliament controlled the navy and south-east England where most of the traders and merchants were only made things more difficult.
Charles strained every nerve to build up his fighting force. He had
never despaired of foreign aid, but one by one his contacts were
failing. His Uncle of Denmark remained unmoved, the French made no
response to his wife's importuning. In an effort to make available
further resources from the family of Orange, the Prince of Wales was
offered as husband to the daughter of Dutch William, but the match no
longer sounded worth the expense to that practical sovereign...
In relation to France and Spain, the Parliamentary diplomatic representative Sir Henry Vane,
proved a far more astute and skilled diplomatist than his rivals and
succeeded in persuading the governments of both countries that the
King's cause was doomed;
Overall, there was a
reluctance of foreign courts to come to the aid of a king who had lost the support of his capital and largest seaport
Source: C. Hibbert, Cavaliers and Roundheads: The English Civil War 1642 -1649
Prince William of Orange even advised Charles
that the best course for the King of England would be to make peace at
any price with his subjects.
It was advice that the King, to his cost, did not take.
Jongchul Kim, 'How Politics Shaped Modern Banking in Early Modern England' at http://www.mpifg.de/pu/mpifg_dp/dp12-11.pdf
Eric Kerridge, 'Trade and Banking in Early Modern England' at https://books.google.co.uk/books?id=1mK8AAAAIAAJ&pg=PA100&lpg=PA100&dq=early+modern+banking&source=bl&ots=jc63OAcjPL&sig=czU34CI8BwjrYZms5DZ_38qml3k&hl=en&sa=X&ved=0ahUKEwjxs-fbuoPXAhXIerwKHTktDrcQ6AEITDAF#v=snippet&q=charles%20I&f=false
Joseph P. Farrell, 'Financial Vipers of Venice'
Geoffrey Treasure, 'Richelieu and Mazarin'