France: still the largest and most powerful European power on land, the French are attempting to recover from severe economic turmoil following the death of Louis XIV. Louis XV was not well trained and experienced for a stable period of rule, let alone one of many crisis.
With the encouragement of numerous nobles loosely associated with a "peace party" Louis XV has chosen to take the path of reconciliation and negotiation. Of course, these nobles happen to own lands on the north eastern border of France and therefore the most susceptible to being ravaged during a war. This fact is well known to the "war party" of nobles who are unhappy with the return of lands once conquered. However, the carrot of the New World dangles in front of all the French nobility, now that they have sole claim to colonies on the Western continent.
France seeks a stable border to her NW. While she still has the largest army in Europe, by far, she is intent on settling the New World and defending her gains. France will entertain any serious offer of agreement with fledgling nations, but at a price, they must keep France's enemies at bay and act as buffer states.
In return, France will consider loaning a few lesser quality units and/or granting financial support (more of the former and less of the latter) to any worthy ally.
France expects such fledgling nations to be Catholic monarchies. Should prospective allies be neither, then the amount of support they could expect is greatly reduced. If not both, then the best such a nation could hope for is a trade agreement; France needs money, after all.
England: a nation on the verge of greatness, but falters and falls short, this is England. Internal upheaval led to external political choices. England suffers from the civil war currently plaguing her closest neighbor, Scotland. In fact, the level of destruction in the lowlands, caused by highland marauders, is forcing large scale emigration by those not tied to hereditary lands. Many of these refugees head to York, where officials quickly put them on roads heading east or south. East, to the ports, is where the poor are sent, to be removed to the Continent. South, to London, is the destination of the landed and relatively wealthy.
The loss of Ireland was probably a better deal for England, if a harsh reality to the English and Loyal Irish subjects living on that island. The new government, a Catholic government, had begun "escorting" traitors and unwanted foreigners to England-bound ferries and shipping almost before James III took the crown. These individuals are shipped with only the clothes they are wearing and sometimes not even that. A few lucky, or prescient, individuals were able to pack up their belongings and head to their own private transport off the island, before the self-appointed purity committees showed up at their doorsteps.
England readily accepts allies that are not bound by ties to Catholicism. Toleration is acceptable, but the English are not currently well disposed towards any nation that recognizes the Papacy as the supreme theological and secular authority. England's armies are exhausted, especially those of Scottish heritage, while half of the Irish regiments have returned home, to save what they could, or to celebrate a glorious independence from England.
England looks to the West, but only unofficially, as new sources of income and room for expansion. Yet, allies on the continent may well serve to keep Channel piracy in check, and other European powers from having any ideas about interfering with English affairs.
Financial support is more readily available to allies; military support much less so, aside from some Scottish or Irish battalions that are, in truth, mercenaries under a national flag. England will establish trade agreements with nations that do not support piracy in the Channel. She looks with some measure of jealousy and revenge towards France and, at some point, England hopes to reduce the power of her Catholic foe.
The United Provinces are no more, instead they are a weak shadow of what what they were and a new nation, called the Dutch Republic, arises from the ashes, in it's place. The Dutch are no longer a major power, but they seethe at having been shattered in a treaty dictated by the other powers. Still an economic center, if greatly reduced, the Dutch will defend their interests rabidly, to the point of attempting to militarily influence the internal affairs of their new neighbors to the south. An alliance with the Dutch will pay off financially and militarily, but at the expense of being seen by the other powers as provocateurs, thus limiting diplomatic access to other major powers.
Denmark: unsure about what to do with the situation to the south, the Danes are fortifying their southern borders. Trade agreements are easily made, but an alliance with the Danes is a rare thing. Religious toleration is expected, as is a certain amount anti-Swedish sentiment. This last can be dangerous as Charles XII sees himself as something of a kingmaker and king breaker. The Danes have little in the way of financial or military support that they can provide, aside from hiring out excellent quality troops, but an alliance with them may well serve to secure a northern border.
Sweden: one is either for Charles XII and Sweden or against them. The Swedes give moderate financial support, but will send an allied contingent, instead of loaning troops. Military success keeps this relationship healthy, otherwise, the Swedes can find better uses for their troops. Charles XII seeks to reconcile with England, freeing his navy to transport troops to the continent.
Prussia: a major power in embryo, Prussia has tough and hardened troops, but no money. Prussia will loan a large amount of troops to an ally, but these must be paid for by the host nation. Financial gifts or tracts of land will make King Frederick even happier.
Austria: next to the Dutch, the Austrians feel most slighted by the Treaty of Paris. Having lost Spain to the Bourbons and with the Elector, the Duke of Bavaria ignoring, if not outright rebelling against the Emperor, Austria stands to lose even more of its German holdings. The Turks are a significant threat, which the other Powers seem to have forgotten, and only Austria holds closed the door to Western Europe. An alliance with Austria has little in the way of tangible rewards, except they do have excellent Hungarian/Croatian light cavalry and a fair amount of heavy cavalry, unlike most of the other Powers. Austria cannot afford to give any financial help as there are signs that a war of reunification against Bavarian lay in the not too distant future. Instead, good quality cavalry, and plenty of it, is available for "loan" in return for financial "gifts" to the Hapsburg throne.
Spain: For all intents and purposes, Spain is a puppet, albeit a sick one, of France. However, approximately half of the Spanish are unhappy with a Frenchman on the throne. There is no point to developing an alliance or even a close association with Spain, given the current political and economic circumstances in the country. But, to act against Spanish interests, such as aiding the disaffected populace, or merely being Protestant, can quickly gain their ire, and eventually that of France, herself.
Russia: Peter, Tzar of Russia, has been agitating against Sweden for some time. Beyond that, it could be said that he has looked upon the doings of the Western Powers with no small amount of glee as it leaves him with more of a free hand in the East. An alliance with Russia, while possible, pays no dividends in Western Europe. One may trade with Russia, but with the distance between borders and with Prussia and the German States laying in between, not to mention, Poland and Saxony, no Russian troops would be able to make that long trek through unfriendly lands. Since the Swedes currently control the Baltic, the Russian navy is not about to attempt to transport troops by sea. Certainly, the Russians would be happy to have someone with who, they have influence, but that someone will wait many long years before ever gaining a benefit from it.
**Confederation of American States of New England**
The English colonies in the New World were hardly thrilled to learn that they now owed allegiance to the French king. Once the provisions of the Treaty of Paris became known, the colonies declared themselves independent from English rule and therefore not bound by the terms of the treaty. A small French army is about to set sail for the new world, intent on forcing the former colonies to abide by the treaty. French Huguenots are aiding the New Englanders with information. An alliance with the Confederation is impossible at the moment, as the French navy is effectively blocking access to and from the newly independent country. Should this circumstance change, an alliance would be completely one way as the Confederation is in need of financial support and military aid; their mere survival is their primary concern.