Hey, this post may be of some use to you for more detail:
Ultimately your intentions are a bit misguided: France and the United Kingdom were not fighting "for world dominance". In the duration of what we could call their rivalry as modern states, let's say halfway through the 17th century to 1815 (Vienna), France would rarely directly get at odds with Britain. It was, more often than not, Britain who intervened against France in a policy of disallowing the continental dominance France was often capable of achieving and, at times, held.
If there's one sentence to describe British continental strategy for basically the entirety of their tenure as a Great Power it's just that -- they would not allow a single power to hold sole dominance of the mainland continent. From the reign of Louis XIV (1643-1715 as ruler) onward that power was France that had to be kept down. As Napoleon rose and France became the preeminent power in Europe, Britain funded her enemies to continue an endless war (Austria and Prussia, primarily) to bring them down.
After the Napoleonic Wars we reach a point where France is neutered. They would suffer revolutions in 1830, 1848, 1852, and 1870/71 and would experience massive economic downturn and social strife. Her colonies were slipping away and this was prior to the rapid expansion into the heart of Africa. In short, she was no longer a threat.
Germany, however, was. Germany was rapidly expanding her navy -- not with long distance cruisers for colonial and trade protection but short range, heavily armored dreadnought-styled battleships. Germany was rapidly expanding its industrial and financial clout, expanding its military, and had just enforced an extremely punitive treaty on France. While France certainly declared war on Germany first, everyone was able to call a spade a spade -- Germany invaded and occupied them for years, enforced massive reparations even though no German territory was touched, and seized significant territorial ground while also browbeating sovereign states like Bavaria into submission through military and economic isolation and threatening the likes of the Russians and Brits with supporting leftist revolution in their borders if they tried to interfere. Needless to say Germany was acting belligerent and was trying to achieve continental hegemony and Britain fundamentally did not like that.
What really sent Britain over the edge was the Moroccan Crisis'. What was quite only an agreement between France, Germany, and to an extent Italy over recognizing North African colonial possessions, Germany intervened hard. To quote from my above post:
In the same year, 1905, the major event which most historians attribute as the first real catalyst that 'set the ball rolling' toward war happened. The First Moroccan Crisis. As we know France was basically given control over Morocco by a mutual agreement with the British and the Moroccan's were not very happy about this and began bustling for independence. Rightfully so they wanted independence I should add as let's not get it twisted, this was French colonialism and it's no different from any other kind. Germany however was not acting in some benevolent fashion and wanted to undermine the French to weaken them and more importantly wanted to draw a wedge in the Entente Cordiale by illegitimizing it. If Morocco attains full independence despite the agreement the two nations are driven apart. Kaiser Willhelm II would go to Tangiers and deliver a keynote speech crying for Moroccan independence and how no nation should fall under the colonial grasp of another. Germany had whispered into the ear of the Sultan to disassociate and rebel against France's wishes and was basically hoping by getting the rest of Europe involved it would go their way and undermine the French to further isolate them from everyone else.
France would react violently. Their Prime Minister obviously insisted that a conference was not necessary and Morocco was under their sphere of influence. Germany would disagree and threatened war over the issue by threatening a defensive treaty with the Sultan. Germany was not going to declare war over the issue, it was a bluff by all accounts and an extension of Weltpolitik. The Germans were not prepared for a war at this point and were merely using their big guns as an extension of their diplomatic body to flex in the French's face. It was aggressive diplomacy and it worked. The Prime Minister Delcassé would resign as no one would support his staunch anti-German policy and agreed to attend the conference. They were, effectively, bullied into submission.
Things were looking up for Germany...but then then they weren't. The conference was totally a disaster and there is no way of twisting it any other way. Nobody supported Germany outright. Russia obviously supported France as did Spain but the real shockers was first Britain and secondly Italy. Wait what? Britain makes sense -- they maintained the integrity of their agreement but Italy was the true shocker. Germany's public defensive ally defied it in the congress and while Austria-Hungary tentatively supported Germany it was with an asterisk basically begging them to please stop being so aggressive and be more conciliatory. Germany, and more specifically the Kaiser, could have taken this as a note of the failure of Weltpolitik as a foreign policy but instead the Kaiser became more solidified in his belief in it. He would not again let himself back down and instead viewed more aggressive diplomacy necessary for it to work.
France and Britain had grown closer and at the very least Germany hoped this would drive at wedge between France and Russia. Well...it didn't. All 3 powers supported the same decision in this conference and recognized the threat of Germany. Britain and Russia who just one year prior were actively fucking each other over began to make nice now and by 1907 would sign a series of agreements which would solidify the boundaries in Central Asia, the fate of Persia, and basically begin their friendship.
This was by all accounts the logical choice for both parties. Britain wanted to support France but to support France they would need to accommodate Russia. Also by extension of this agreement Britain would free up swathes of manpower stationed in India which were there for a significant purpose of keeping Russia in check and contesting said Central Asian territories. Although Russia herself could still go back into Germany's arms any time she wished in this period and really did not need the French and British as much as they needed Russia, Russia felt alliance with the two powers was more beneficial than with Germany and A-H. The catastrophe in Manchuria against the Japanese and the failed revolution in 1905 as well showed the Tsar that the frontiers needed to be handled once and for all and the efforts concentrated and by dealing with Manchuria with Japan via losing and by dealing with Central Asia with Britain via diplomacy Russia could exert all of her efforts toward the West.
Once the Second Moroccan Crisis happened and the Germans once again intervened in a sovereigns internal matters with their warships, Britain had a collective national meltdown. Not only was Germany intervening in sovereigns continental matters, she was now using her navy as a power projection force, ie gunboat diplomacy. Even worse the British didn't even know where the German navy was! So this combination of German military and economic hegemony on the continent, clear naval aspirations directly contending with British interests, along with them using their navy to mess with others (that was Britain's job in their minds!) and British thought thoroughly shifted to anti-French to anti-German.