We're talking about whether or not the sofa seller should be allowed to live down the block, not in your house. Right now, if the sofa seller wants to work for peanuts in a third-world country and outsell local manufacturers in, say, the US; they have the right to do that thanks to literal decades of trade negotiations. But if they want to play fair and compete on a level playing field in the US, they have to get visas in restrictive categories and wait in long queues. That's because there's far less international law on liberalizing the market for labor.
Furthermore, the EU doesn't have Free immigration. EU freedom of movement is only extended to member state citizens; and the Schengen area only dissolves "internal" border infrastructure. Both of those schemes are predicated on the existence of "external" borders which are not opened. If you don't already live in the EU, you're subject to the same types of visa categories and quotas you'd get if you were trying to immigrate to the US.
The reason why it seems like the EU has Free immigration is because there was a refugee crisis a few years back. This is, again, not Free immigration - it's just a particular visa category everyone agreed to for various historical fuck-Hitler reasons. You still have to actually prove to an immigration judge that you have a case of being a political refugee, which is far harder than most people think. Meanwhile, economic migrants still have to go through the process of getting work visas for particular approved professions, sitting on quotas, and so on and so forth. So you get none of the benefit of a Free immigration system but all of the downsides of political, economic, and racial ressentiment, etc.