Palmer, aged 20 from Horsham, finished in second position in the highly respected 2.0-litre single-seater category’s first race of three at Spain’s Barcelona Grand Prix circuit.
However sixth and fourth place finishes in races two and three were not quite enough to stop France’s Sacha Fenestraz from becoming the new champion.
Palmer’s results for the season include three wins, including an outstanding victory in support of the Monaco Grand Prix, as well an additional seven podiums finishes.
"It's been a great season and I think I can be proud to finish as vice champion in such a competitive championship,” commented Palmer. “R-ace GP (his team) have done a great job this year, winning the team's title and I have learnt a lot working with them do I have to say a massive thanks to them as well."
Finishing sixth and seventh in the final standings were fellow Britons Max Fewtrell and Dan Ticktum. Fewtrell, aged 18 from Birmingham, took the championship’s rookie title and said: “Winning it underscores our performance in our maiden season in Formula Renault Eurocup. The field was made up of some incredible drivers and I was still able to take my first win and fight for podiums. I hope I can use this opportunity next year to aim for the title."
Notably, Red Bull Junior driver Ticktum, also 18 from London, has since gone on to win the famous Macau Formula 3 Grand Prix race at his first attempt.
Both he and Fewtrell have also been shortlisted for the coveted McLaren/Autosport/BRDC Award for rising young talent – the winner will be announced in London on 3 December.