The 40-year-old Bruni herself told the Liberation paper earlier this week that she would not be accompanying the president as they were not yet married.
Foreign ministry sources in conservative India had raised eyebrows over the prospect of Bruni attending as first lady due to protocol issues.
The romance has some French worried their president is neglecting his election pledges to slash unemployment and boost growth.
The Taj Mahal was built by Emperor Shah Jahan as a tomb for his beloved queen, Mumtaz Mahal, who died while giving birth to their 14th child. About 20,000 workers toiled for more than 20 years to build the tomb.
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