What if Japan was influenced by France rather than Britain in the late 1800's and created an alliance with France instead of Britain?
I think for this to happen, you would need a POD well before the Meiji Restoration. Japan was more or less forced to opened up after Commodore Perry's Black Ships visited in 1853 and 1854 and of course, this led to the fall of the bakufu, the Meiji Restoration and ultimately to Japan's rapid modernization.
One of the major catalysts for Japan's modernization was to catch up technologically with the West in order to renegotiate what it saw as unequal treaties that had been negotiated between the Tokugawa bakufu and the Western powers. Three years after full power had been restored to the Emperor, in 1871, a mission was launched to travel the world (the Iwakura Mission) in order to do two things: renegotiate the unequal treaties and to view what countries did what best (technology, government, military etc.) and to bring the best learnings back to Japan for Japan to implement. The Iwakura Mission travelled from Japan to the USA, then on to the UK, Europe, Russia and SE Asia.
Whilst the Iwakura Mission ultimately failed in renegotiating the treaties in place with the major Western powers, it was able to view and compare the best examples of modern military, technology and more across a number of countries. Japan pretty much correctly identified the best examples (at the time) of most modern institutions and borrowed the ideas, changing them where necessary to meet Japan's own cultural needs, to build up its own infrastructure and reform. Not only this, but Japan invited experts from each of these countries to Japan to assist with implementing and building up this infrastructure. So Japan took and used experts from Prussia / Germany to build, train and develop a land army, education experts from American and Prussia / Germany to build an education system, naval experts from the UK to build and develop a strong navy (this developed into the UK-Japan Alliance and as a side note, is the reason that the Japan Maritime Self Defence Force to this day eats 'kaigun curry' every Friday), railway experts from the UK, agriculture experts from the UK, legal experts from France to develop a civil and criminal legal system and experts from France, the UK and America to develop a parliamentary system, which resulted in the Diet.
So all of this is why I think that for Japan to borrow more from France and to develop a stronger link or alliance with France, an earlier POD than the Meiji Restoration is needed. Providing that any earlier changes do not butterfly the Meiji Restoration away and it goes ahead as per OTL, you need to see a much stronger, much more developed France. So think of a France with a stronger navy, stronger army, more industrial might and more. This would need a POD along the lines of there being no French Revolution or Napoleon winning the Napoleonic Wars or fewer revolutions and changes in the 19th Century that impacted society.
Don't forget that in 1871, the first year of the Iwakura Mission, France had just been defeated by Prussia in the Franco-Prussian War. Showing weakness and such a defeat is perhaps one of the reasons that French military prowess was not so admired by the industrializing Japanese and to be able to have more of an impact and more influence, France really needed to have a stronger military and industrial base in place well before 1871. If that had been the case, we may have well seen an alliance with France rather than Britain, or maybe Japan becoming part of a triple alliance with France and Britain.
However, having said that, one thing does kind of wave away any of this. Japan saw itself as potentially becoming an Asian version of the UK. It saw many similarities; it is an island nation that needs to protect the waters around it, it has large, potentially aggressive continental neighbors and, of course, it's another of the world's greatest tea drinking nations

Jokes aside, France did not really need to have as big a navy as the UK and for this reason, Japan saw the UK and the UK's imperial success as an island nation as a very relevant Western power to copy where necessary and to ally with until it was strong enough to be an imperial power in its own right.