The medal is Spendrini-Siriex's first individual medal at the world championships and follows her gold medal in the team event on Saturday.
Teenager Lois Toulson became the first British woman to win a world diving medal when she won silver in the 10m synchro event last year.
Toulson finished sixth in Monday's individual final, with China's Olympic champion Quan Hongqiang taking gold and compatriot Chen Yuxi, the defending world champion, taking silver.
Quan and Chen dominated the competition with 436.25 points and 427.80 points, respectively, while Spendrini Sirieix, the daughter of French maître dre and TV personality Fred Sirieix, took third place with 377.10 points.
Thorpe and Shortman, who performed a routine inspired by London landmark Big Ben, finished second behind China's Wang Liyi and Wang Qianyi, with Spain's Alisa Ojogina and Iris Tio taking bronze.
“It means so much more than words can describe,” Thorpe said. “We can only hope to inspire young girls and boys back home that we can lead the way for them and that there is a bright future for British artistic swimming.”
Shortman added, “Hopefully we can promote the sport a little bit more and encourage people to participate in everything that comes with it.”
Last July, Shortman made history by winning the bronze medal in the solo free final at the 2023 World Championships in Japan.
Thorpe and Shortman will compete again on Wednesday in the preliminary round of the free duet event, with the final to be held on Friday.
The scores from both finals will be combined to determine qualification for this summer's Paris Olympics.