This isn't far fetched. France and Prussia had long been allies against the Austria, Britain/Hanover, Netherlands alliance.
Basically, France and Prussia were allies by default as the other powers were allied against them. France's endless conflicts with Britain over the Americas didn't concern Prussia. Prussia's conflicts with the Habsburgs didn't interest France. It was an enemy of my enemy type deal.
It was the severing of the Austrian and British alliance that had protected Hanover for years in the face of Prussian aggression. After the War of Austrian Succession, where Britain did little to support Maria Theresa, she saw no major benefit in supporting Britain and the alliance dissolved. They also did nothing to support Austria in the War of Polish Succession. The Netherlands was declining and was depending more and more on neutrality than arms to protect themselves and would not again play a major part in European affairs.
As is, the Austrian/French alliance was still surprising given their centuries of rivalry over the Holy Roman Empire. It was considered "unnatural". However, Frederick the Great had enraged Maria Theresa by seizing Silesia. There was little chance Britain could or would do much to get it back. The alliance with France was convenient, guaranteeing at least French neutrality in the next war with Prussia.
Britain and Prussia, two countries that didn't like each other, pretty much were forced into an alliance or risk being without allies in the face of a war with a larger land power (Britain against France, Prussia against Austria). It protected Hanover from France (and Prussia).
Meanwhile the relations between Austria and France had improved. Habsburgs no longer surrounded France with the "War of Spanish Succession". Austria was unlikely to pose a threat to France and Louis XV had little interest in the Holy Roman Empire. Basically, they formed a defensive alliance because they no longer had a reason to be rivals.
How to maintain the French/Prussian Alliance?
1.
If you want to go back a ways, then maybe Britain might support Maria Theresa more. If she kept Silesia in the 1840's with British assistance (either troops and/or more gold), she may have seen the alliance in a better light. Also, Frederick would not have been much of a threat to Austria without Silesia's population, wealth and resources.
2.
Start an early war between France and Great Britain, say earlier in the 1750's. before the "Diplomatic Revolution" ever occurred. Austria and Prussia may not want to getting involved in a war started for reasons not their own. The Germans were always going to fight each other again but at the time of their choosing, not Britain and France's.
The 7 years war may play out much the same, with GB and France going at it in Hanover and America, while Austria and Prussia tussle on their own. Two completely separate wars occurring simultaneously.
I suspect the outcome would be largely the same.
France never got involved much with Frederick's armies as they were fight GB/Hanover/Brunswick in Hanover and America.
Austria was the primary antagonist against Prussia. Sweden was a sideshow.
Really, only Russia's involvement was uncertain.
Had Frederick not pissed off most of Europe with his sneak attack on Saxony, then Russia, Sweden, Bavaria may not have jumped in at all.
As is, it really was a miracle that Frederick lasted long enough to see the "Miracle of the House of Brandenburg". He should have been crushed a dozen times over by superior numbers of Austrian/Russia/Swedish/Bavarian troops.
If the Russians hadn't been so ponderous, and the Russian and Austrian Generals had cooperated just a bit more, then Frederick would have been destroyed by 1758.
His Empire would have been dismembered with Austria, Saxony, Russia, Sweden and France all taking a share.