In general, when traveling the following areas, what is the best non-English language to know? Or is it english after all?
In continental Europe?
In southern Asian? ex. Vietnam, Cambodia, Laos, Thailand, Indonesia, Phillipines
In Africa?
In the middle East?
The Africa one is pretty easy - the answer is French. About 20 countries in Africa have French as an official or quasi official language. In many of those counties, English speakers are quite rare. French isn’t just useful, it is basically essential.
I’m pretty sure southern Asia is English, except maybe places like Laos, Cambodia, and Vietnam.
I suppose French, but that won’t really help you that much in Spain, Italy or Germany unless you happen upon someone who speaks some French. Most people know at least a little English, but it’s hit and miss that someone who doesn’t natively speak a particular language will know it. The exception to the rule being Belgium and Switzerland where multilingual speakers are very common. Lots of people in the Middle East, and India are taught English as kids.
And French will help you in Vietnam and Cambodia I believe.
I’ve always heard that French and English are the best pair for traveling the world.
In the Philippines the best language is definitely English. I don’t think that any other language will do you much good. Older people may know some Spanish, and Tagalog has absorbed a lot of Spanish words from when it was a Spanish colony, but Spanish won’t help all that much.
English was generally useful to me in Indonesia, Malaysia, and Singapore. Because Indonesia and Malaysia are Muslim, you might be able to find a few people who know Arabic (as the language of the Koran), and Bahasa Indonesia has a lot of Arabic loan words. Singapore is majority Chinese so the most useful language besides English is probably Mandarin. The Chinese are also the largest ethnic group after Malays in Malaysia.
In Africa, as has been said the best other language is French.
Well, the Old World. Obviously in the Americas English and Spanish are the best.
Going around SEA countries and meeting the ethnic Chinese in those countries, I find that most of them are from the southern part of the mainland and speak Fukien. Very few know Mandarin / Haka, even those in Hong Kong, where most speak Cantonese.
In Central Europe, German. In western Europe, “universal Mediterranean”, which is a blend of schoolboy French, Italian, Spanish, Catalan or any other Romance language. This will get you by in a lot of places.
In East Africa Swahili is pretty useful too.
Wiki says modern standard Arabic is the third most internationally understood language, after English and French.
Depends where in the New World. Spanish isn’t much help in Canada.
Actually, lots of non-native-French-speakers in Belgium and Switzerland will prefer English over French. I’ve even encountered some who took offense at being addressed in French despite being in a French-speaking area (dude, not my fault you’re a jerk).
In Spain people over 50 with a… let’s say, HS-equivalent education, are more likely to speak French than English. But most of the people you’ll encounter in tourist or business settings will speak English, with levels varying between “what, you’re not American?” and “aserejé”. And we have lots of multilingual speakers, it’s only that the languages they speak well may none of them be a foreign one.
If you’re going to confine your travels in the Americas to Quebec, Haiti, and a few small islands in the Caribbean French is useful. If you plan to travel widely in the Americas, not so much. If you wanted to pick a third language besides English and Spanish, Portuguese would be a much better choice than French. It has 10 times the number of speakers that French does in the Americas, and is spoken over a much larger total area.
According the the Argentine and the Brazilians I’ve worked with, Spanish and Portuguese are sort of mutually comprehensible, and there’s a hybrid called “Portunol.” So maybe Spanish would get you by in Brazil?
Some day I’ll learn how to add a tilde.
It is if you meet both of the Spanish speakers in Canada on the same day. 
I got around Spain pretty well with my bad French. Spaniards who don’t know English are a dab hand at bad French.
Oh, bad French is easy! It’s good French that Spaniards suck at.
Write it with the Portuguese spelling instead: Portunhol 
My experience in Brazil was that I had very little trouble with people who had a HS or higher education, but I needed an interpreter at the supermarket. Good thing “point and smile” works everywhere!
I speak Spanish and have traveled in Brazil. It helps a little but not a huge amount. I could get the gist of newspapers and other written material, and to some extent newscasts and lectures where people spoke clearly and distinctly. But the different cadence of Portuguese makes it difficult to understand conversationally, at least for me. It would no doubt be somewhat easier for a native Spanish speaker.