Assuming that you bought the MBP in 2013 back when you were discussing it here on TS, and that you bought one of the last 2010 models (in 2011, they dropped the Core 2 Duos and went to the i series processors) and never updated the OS, then you CAN update the OS to 10.13 - High Sierra, which is the last OS before the current one (Mojave, 10.14) But, you do need to have sufficient RAM and while it will theoretically run with 4GB, which is what most of these machines had when shipped, it will work better with 8GB.
I believe, from reading some of your old posts on TS, that the reason you wanted the older machine was because you had older hardware and software you wanted to continue to use. Is this no longer the case?
If so, then my advice is the same as it is to pretty much everyone: to go for the best combination of features and speed that you need, and can afford. You can get some good deals on the refurb store here, but the one in France seems to have only a few items available. Not sure why. Same thing with the refurbs in the UK, Belgium and Germany. A few in the "featured" section, but NOTHING at all in the main Mac refurb section (if you look at the Canadian store -
https://www.apple.com/ca/shop/refurbished/mac - you'll see the huge difference. It's bizarre...)
Anyway - if you can post your current specs - do the "About this Mac" thing - processor speed, RAM, hard drive capacity - Model number so we can check things on
https://everymac.com (or just post the link to the right one at everymac.com) that would help a lot.
You can certainly update the current machine so you can run current browsers and so on - but if you need to keep it as is to use with some old hardware/software and want to buy a new one to run current software/browsers/hardware, then we need to know what you want to do with it in general terms and what sort of budget you have in mind.