I just returned from my first river cruise -- the Danube on Avalon Envision. I traveled for first time as a single (age 65, male, recently divorced) and wasn't sure what it would be like after 40 years of travel with spouse and/or family. It was great and I recommend it to others.
I found it rather easy to meet others, and I am not an extrovert. The variety of people I met and conversed with was among highlights of the trip. I found there were people who sort of watch out for single travelers. At dinner the first night I sat by myself at a two-top but was adjacent to two couples I met on the bus from Prague to the port. It probably appeared that I was "all alone" and soon an outgoing lady from a nearby table got up and came over and introduced herself and told me about the group she was traveling with. Very nice gesture. In the next few days I found myself "adopted" by two other groups of four people and tended to hang out, do excursions and have meals with them. (They were varying ages, and one was asked by another cruiser if I was their uncle, because we were hanging out so much). By the end of the week we knew everything about each other's backgrounds and families and will stay in touch. It was easy. Just ask others that you come in contact with if this is their first river cruise (I found that it usually was), and conversation flows from there.
By the way, the no-single-supplement is capacity controlled. There are only so many "single cabins" per sailing, so be aware. You can track the availability on the Avalon website, for example (although I used a travel agent to book). The no-supplement is highlighted in yellow if available for a particular sailing date. I just booked Paris to Normandy for May 2020 the day before leaving for the Danube. I planned to wait until I returned, in order to see how I liked river cruising before committing, but was tracking availability for several dates and noticed the no-supplement was starting to dry up for spring 2020. So I jumped in (deposit only $250, what the heck). When I returned, there was no single availability for my three weeks of choice, so it was the right decision not to wait. For this early May 2019 trip, there was single availability when I booked in late July 2018. But the Danube has more ships/capacity than the Seine (Normandy), according to TA. Some cruise lines, such as Viking, do not cater to singles, FYI.