A leg spinner, Francke played for Ceylon in 1957/58, and worked and played cricket in England for several years prior to migrating to Australia. He reports having had offers to play first-class county cricket in England but chose not to because it would have been a full-time commitment requiring him to suspend his career as an accountant. He represented Queensland from 1971/72 to 1985/86, making his debut against a touring World XI side. Francke dismissed Clive Lloyd twice and also took the wickets of captain Rohan Kanhai and Sunil Gavaskar. He went on to take a total of 167 career first class wickets for Queensland with an innings best of 6 for 62 against South Australia in 1974.
In 1975 he was part of a rebel tour of South Africa, playing for the Brian Close-led DH Robins XI.
Leading Australian spinner Ashley Mallett considered Francke to be the best legspinner in Australia during his time and was disappointed Francke never played Test cricket. He had been mentioned in particular as a test chance in 1972/73 and 1973/74 and 74/75.
In September 2018, he was one of 49 former Sri Lankan cricketers felicitated by Sri Lanka Cricket, to honour them for their services before Sri Lanka became a full member of the International Cricket Council (ICC).
- "Six team changes by Queensland". The Canberra Times. 17 November 1971. p. 32. Retrieved 15 December 2014 – via National Library of Australia.
- Chappell, Ian (January 1977). "England 1977... Ian Chappell Predicts". Cricketer. p. 21.
- "Qld reels against Sth Australia". The Canberra Times. 23 December 1985. p. 36. Retrieved 15 December 2014 – via National Library of Australia.
- "Kiwi top-order puts India on the slide". The Canberra Times. 24 January 1986. p. 1 Section: SPORTS SECTION. Retrieved 15 December 2014 – via National Library of Australia.
- Mallett, p. 158.
- "WEST INDIES TOUR Test hopes have days left". The Canberra Times. 15 December 1972. p. 22. Retrieved 15 December 2014 – via National Library of Australia.
- "Queensland hopes rest on Chappell". The Canberra Times. 6 February 1974. p. 28. Retrieved 15 December 2014 – via National Library of Australia.
- "Test selectors prefer experienced players". The Canberra Times. 25 November 1974. p. 16. Retrieved 15 December 2014 – via National Library of Australia.
- "Sri Lanka Cricket to felicitate 49 past cricketers". Sri Lanka Cricket. Retrieved 5 September 2018.
- "SLC launched the program to felicitate ex-cricketers". Sri Lanka Cricket. Retrieved 5 September 2018.
- Mallett, A. (1993) Clarrie Grimmett: The Bradman of spin, University of Queensland Press: Brisbane. ISBN 0 7022 2531 2.