The 109th-ranked player from Kaohsiung now lives in Paris, where she met her boyfriend last year, and she is also rekindling a love affair with the French clay.
Hsieh, 31, won the women's doubles title at Roland Garros in 2014 but has never previously got past the second round in the singles.
Having kicked off this year's run by dumping out seventh seed Johanna Konta, Hsieh would claim a berth in the last 16 of a grand slam for only the second time in her career if she bested 28th seed Garcia.
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Following Hsieh into the circular arena of court one will be two of the top three in the Asian men's rankings.
Japanese eighth seed Kei Nishikori will begin as heavy favourite against 67th-ranked Chung Hyeon - but a win for the bespectacled South Korean might benefit the sport's regional profile more.
(Reporting by John Stonestreet, editing by Nick Mulvenney)
