I'd suggest that there's little point in trying speed tests on the existing, questionable, router or on someone else's line. What needs to be done is to beg, borrow or steal (or buy) a decent ADSL router and try that. Preferably try a speed test to a known source on both routers, for comparison purposes.
It may be that the PhoneExpat router was rented from them, in which case they should send you a replacement, but if it was purchased outright you're on your own. To choose a suitable router, one site to look at is bestrouter.co.uk. Their Best Buy for under £50 is the TP-Link TD-W8968, which is available from amazon.fr for €39.90, which seems a good deal to me. Personally, I'd avoid Linksys ADSL routers, but I've had three early failures with them, so I might be biased.
Installing the router should be fairly straightforward, but you often need to set up the technical parameters in line with your existing account. These should be available inside the old router but you'll need to note them down. If you have a local computer technician service, you might prefer to get them to do it for you. It should be possible to take both routers to them & they can configure the new one. You might also consider buying a router from them & ask them to set it up as part of the deal.
Why did this happen? Several possibilities come to mind:
Linksys routers seem to have a short life anyway; Other routers may be similar. Liveboxes & SFR Boxes last a bit longer, but often fail after, say, 5 - 6 years.
My best guess would be that you had some thunderstorms recently & a surge on the phone line damaged the router. In essence, your router is the device at the end of a long copper wire running from your local 'phone exchange. Lightning can induce strong currents on the wire which find their way to earth through your router, Hence I'd strongly recommend putting a telephone surge protector in the line before it goes into the router. (This surge protector must be earthed, or it can't do its job. Easy if you have modern wiring; much less so if you have only two-pin sockets.)
Bon courage with it