It's worth pointing out that in France and the UK, the authorities involved are arms length independent of the political bodies - it's not like the US where if you give the President good vibes you can become head of the FBI, and all you have to do in return is whatever he says. There are statutory instruments (in France, constitutional clauses), that determine the independence of these authorities.
They are tasked - and held to account by respective legislative bodies - with implementing the law as written.
Nobody wrote a law saying "Go after Grok". There is however a law in most countries about the creation and dissemination of CSAM material and non-consensual pornography. Some of that law is relatively new (the UK only introduced some of these laws in recent years), but they all predate the current wave of AI investment.
Founders, boards of directors and their internal and external advisors could:
1. Read the law and make sure any tools they build comply
2. When told their tools don't comply take immediate and decisive action to change the tools
3. Work with law enforcement to apply the law as written
Those companies, if they find this too burdensome, have the choice of not operating in that market. By operating in that market, they both implicitly agree to the law, and are required to explicitly abide by it.
They can't then complain that the law is unfair (it's not), that it's being politicised (How? By whom? Show your working), and that this is all impossible in their home market where they are literally offering presents to the personal enrichment of the President on bended knee while he demands that ownership structures of foreign social media companies like TikTok are changed to meet the agenda of himself and his administration.
So, would the EU like more tighter speech controls? Yes, they'd like implementation of the controls on free speech enshrined in legislation created by democratically appointed representatives. The alternative - algorithms that create abusive content, of women and children in particular - are not wanted by the people of the UK, the EU, or most of the rest of the World, laws are written to that effect, and are then enforced by the authorities tasked with that enforcement.
This isn't "anti-democratic", it's literally democracy in action standing up to technocratic feudalism that is an Ayn Randian-wet dream being played out by some morons who got lucky.