IMHO the issue is that in Europe, or most of it, you had Latin as the language of the Church and the educated for a long time after the Roman Empire went away. This meant that something based on Latin was going to be easier to be a lingua franca. Written records (bills of lading, credit documents, etc) are part and parcel of a lingua franca. With Chinese, not only is written Chinese extremely difficult, but culturally there was no push to simplify it - the educated classes retained wealth and privilege because only they were adequately literate given the effort it took to become literate. One reason why at some point the Koreans invented the written form of Hangul, which is like the Latin, Hebrew, Arabic, Greek, Cyrillic etc alphabets, phonetic. Another strike against Chinese is to reverse the overall policy of non-exploration/expansion - let the barbarians come to the Celestial Kingdom to trade, not the other way around.
I can't peak to tonal languages, but IMHO even with poor grammar you can make yourself understood in a non-tonal language than with a tonal one - and even today spoken Chinese is difficult between regions after a lot of effort to standardize it. Yeas, English has a lot of weird stuff, but my experience is that non-native speakers, even with bad accents and poor grammar can be understood a lot easier in English than many other non-tonal languages.
English is not based on Latin (though distantly related and still heavily influenced by it and its derived languages), and it managed to become lingua franca anyway.