I definitely not agree with the theory than Chinese/Mandarinian is important, maybe in East Asia, but not in Europe, Africa, Americas. Chinese culture is very closed, China is rather closed country, except of Singapore and Malaysia, there is very "few" (for Chinese standards, naturally)Chinese, living on other continents. And it is too hard to learn for foreigners to become a lingua franca.
English became lingua franca, due to 2 reasons, rise of United States and its global presence, huge economic power, trade. British Empire is the second reason, because of its expansion, English is widely spoken in Africa, India.
I wonder, which language would become a lingua franca, if France had won 7 years war with Britain. Canada would have become French, the same as whole North America, India. Maybe USA or some other country,existing there, would be Francophone.
I also wonder, if Chinese started colonization of Americas in early 15h Century (under Zheng Ho), maybe Chinese would have become a global lingua franca, then.
I agree with the predesessors. English is the most universal, but there's some quite important languages which one needs to know, if you want to travel somewhere freely.
French - except of Western Europe, it is useful in Romania, North Africa (Maghreb), maybe Syria, Lebanon, eastern Canada (Quebec), Carribean, Africa, maybe in the Pacific Islands or Indochina (Vietnam, Cambodia)
Spanish - Latin America, next to Portuguese (which is also useful in Angola, Mozambique)
Russian - definitely lingua franca in post-Soviet space, for me, even more important and much more useful than English, including EU countries like Lithuania, Latvia, Estonia
Arabic - whole Arabic world
Mandarinian - except of PRC and Taiwan, useful also in Singapore and Malaysia.
This is theory, in fact, everything depends from the situation. For example, in Hungary, German is more useful than English, in Italy or Spain, French more useful than English and vice versa (for example Italian in France, Spanish in Italy). In Lithuania, near Vilnius Polish is useful because there's a lot of Poles, living there, the same in western Belarus and Ukraine (if someone doesn't speak Russian but have some rudiments of Polish).