Yes, what Flint suggested is good to test the battery condition but there’s other things to try. With a multimeter set on Volts and the engine running, test across the battery posts actually on the lead posts for the voltage. It should read 14.4v after starting. If it is less, try across the terminals that are on the battery posts. If no different then try wiggling the plug on the back of the alternator and see if the voltage improves. Take the cap off the big connection on your alternator and test from there to the engine block. Again the voltage should be 14.4 or slightly more. Again try wiggling the plug. If still nothing near the 14.4v then you will probably need a new alternator but check the belts first.
In this situation, I would buy two new batteries in France and a Ctek battery charger. Keep the old batteries and fit the new ones. You will get some miles out of them and if the alternator charging voltage is 14.4v then job done. If not then you may need to stop and charge the batteries. To be sure, you may need to take an alternator and V belt with you from a supplier in Romania and perhaps see if you can return it if you don’t need it.
At least it should be cheaper than arranging a trailer and you will at least have new batteries to show for it.
Just to add a bit to Richard's
@StarCruiser 's post, if youre not getting the 14.2V with the engine running, don't immediately blame the alternator.
I has the same issue, bought 2 new Varta batteries and when they were only showing 12.6V charge the battery guy was assuring me the batteries were good and the alternator needed changing.
I then took it to GTC and they tested the new batteries and they were dud.
They kindly fitted 2 new Banner batteries on a sale-or-return basis to try for 30 days. They worked perfectly.
I took the Vartas back to the battery guy and insisted on a refund. He was a pain in the ass, arguing that they were ok, he even "tested" them with a meteor showing 11.9V (disconnected from the truck) and verified them as good
.
I kept insisting on a refund and refusing to remove them from his premises. Eventually he gave in and refunded me, and the Banners have been on the truck ever since (about 18 months if I remember correctly).
The charge Voltage has been steady since then at between 14.3V and 14.0V and I've had no problems.
I hate electrickery, it's a black art to me and sadly the experts are always willing to dupe you.
Only a dead-load test will verify the batteries, the Volt multimeter test is good to verify the charge Volts, as Richard suggested. I suggest you take his advice but buy batteries from a reputable seller, not an onion seller on his bike.