Can I shut down my company in France and open up in UK?

I am interested in your opinion (and others). I’ve had a French registered SARL holiday rental business since 2004. Technically I am an immobiliere with carte professionelle. This allows me to be insured and hold clients rental payments and then pay owners. I am fully registered and have 4 employees (CDI) and pay my tax, social charges, RSI, Tax Fonciere, TVA and every other charge here in France. I also have a shop front. I am willing to compete fairly and of course pay my taxes fairly. But I’m not sure how level the playing field is.

Why are so many of my competitors not registered in France and allowed to trade here renting apartments / villas? Often they are registered as a UK company or maybe not even registered. They have no accountability and less costs. I was inspected by tax inspection and I asked why don’t you go after these non registered people - she replied - you have an office so we can come in. If someone is trading from home with a website, we cannot enter.

On a slightly different note (but similar angle), I read that Starbucks makes a loss in France. But no worries as its makes loads of money elsewhere (US) and pays its corporation tax in US. How can this be if you have a small coffee shop (having to pay all you tax in France etc.) how do you compete with a company that can afford to make a loss - as globally they have profit and pay their corporation tax elsewhere etc.

What I am getting at is as every cost, tax and charge is rising. Is the state not actually targeting companies that are operating in France but not actually paying any contributions. Or, is that just the way it is and they are trading in fact legally either via a loophole or genuinely allowed to.

And my final question, dependent on answers to above. Can I shut down my company in France - open up in UK - and keep website name - no-one sees any difference - apart from your bank balance?