Not that I feel a particular need to defend Russkies here bro, but ...
Re: France/Italy programs, we talk about two world-class marine powers, so there is nothing strange that they can construct&build relatively successful units.
France's and Italy's defense budgets combined are bigger than the Russian one.
Both nations are well established naval construction players for centuries, and none of them faced catastrophic events like the dissolution of the WarPac and the SU itself.
Russkie are being continuously deprived of the possibility of a stable fleet modernization program, and that is both obvious and notorious.
The 2014 coup was a giant blow to the Russian naval programs of all sorts, and I am impressed - frankly speaking - that they have managed to recover in a really short time.
Yet, FREMM is just an oversized equivalent of a Russian corvette.
It represents no bigger punch than 20380, objectively speaking.
From this perspective, Russians made no worse - 20380, 20385, 20386, 11356 ...
If we take let's say Horizon frigates, then again Russkie are not worse with 22350...
Just take a look at the submarine construction program - what the Russians do there is mindblowing. There is no equivalent in Europe for that, no matter that the European combined defense spending fourfold the Russian ones.
lancelot has a good point there.
Chinese are just steadily expanding their capabilities, and that reflects the general condition of China itself.
They became a global superpower in the last 2 decades and the biggest economy on the planet. They need a big, blue water navy because of the structure of the economy - big dependence on the sea route trade.
That includes both the things they export and the crucial resources that they need to import, including the supply from Africa.
It didn't take out of anywhere, you know. They needed time to master the situation, and a civilian construction peak was one of the reasons here. You need cadres to make a successful naval construction program, and you can't have those cadres with no big & effective marine construction sector. This is what Russkie have been building for more than a decade now, and belive me my friend, you will see the difference very soon.
It is a matter of priorities if you ask my opinion