One possible circumvention would be to use the following formulation:
Wenn du jemanden mit dem Familiennamen Frigon kennenlernst, dann kann diese Person aller Wahrscheinlichkeit nach ihre Wurzeln bis nach Neufrankreich zurückverfolgen.
As others have noted in the comments, this implies the feminine (grammatical) gender, and some may thus not see it as a solution.
However, I think that the root of the discomfort that gendered phrases like the one in your original sentence bring about is caused by the specific use of "er" or "sie", which are personal pronouns and are perceived to correspond more closely to biological gender (although they are still grammatical genders). Therefore, by using the noun "Person" you avoid the personal pronoun issue altogether. And as an added bonus, you still can use jemand in your primary clause.
Addressing OP's further remarks:
Among a certain crowd in all languages with grammatical gender there have been discussions of different solutions. However, due to the nature of language use and the broad political spectrum, there has been no concurrence (with perhaps the notable exception of Sweden which has added a gender-neutral 'hen' to the official national encyclopedia) across the board. For example in Spanish there is the use of the @-sign to correlate with both feminine and masculine adjective endings.
German language officials in the German-speaking countries of the world have not yet codified any of the proposed solutions (although, in Germany gender inclusive language has been requested of public bodies), so the use of one of these would be much akin to what you have referred to as an "incorrect" usage of 'they' for the second person singular by English speakers (which I for one am now completely accustomed to and have been using for years now). More information about possible solutions for gender neutrality in German can be found in this question.
Wikipedia Entry: Gender neutrality in languages with grammatical gender
Wir brauchen einen erfahrenen Informatiker.
Stated twice (hendiadys):
Wir brauchen eine erfahrene Informatikerin oder einen erfahrenen Informatiker.
Wir brauchen eine/n erfahrene/n Informatiker/in.
By highlighting the suffix -in:
Wir brauchen eine erfahrene InformatikerIn;
sometimes Wir brauchen eineN erfahreneN InformatikerIn. This is considered bad style, although sometimes used.
Grammatically masculine form, with indication that two genders are implied:
Wir brauchen einen erfahrenen Informatiker (m/w).
Frequently, too, job ads will use a pseudo-English term to avoid the issue:
Computer-Scientist (m/w) gesucht! "Computer scientist (m/f) sought!"
Article on Deutsche Welle: German university opts for gender-neutral language