The princess, a distant cousin of King Felipe VI, was 86 and died in Paris on Thursday, her brother said.
Her funeral was held in Madrid on Friday.
As of Sunday a total of 2,606 people in France had died from coronavirus, France's director-general of health, Jérôme Salomon, said, marking an increase of 292 deaths in 24 hours.
France recorded a total of 40,174 confirmed cases of the virus Sunday, according to the French public health website. That's 2,599 more cases than on Saturday, marking a 6.9% increase -- a smaller rise than the past several days.
Spain has also recorded a smaller percentage increase in case numbers in recent days. The country has recorded more than 80,000 cases and 6,803 deaths, according to figures from Johns Hopkins University.
The British royal family has also been affected by the global pandemic.
Prince Charles, first in line to the British throne, tested positive for coronavirus on March 25. Charles, 71, is currently self-isolating.