On the second day of their whistle-stop visit to the UK, French President Nicolas Sarkozy and his new wife Carla Bruni-Sarkozy had a date at 10 Downing Street.
The Sarkozys bid farewell to their Royal hosts at Windsor Castle, where they spent the night after a state banquet.
The Queen said the countries had a "respectful but competitive relationship".
Ms Bruni-Sarkozy gave her husband a round of applause after he addressed both Houses of Parliament on Wednesday.
Mr Sarkozy also laid a wreath at the grave of the unknown soldier at Westminster Abbey.
The Sarkozys were given a personal tour of the French works in the Royal collection at Windsor Castle.
Mr Sarkozy was also invited to review the Guard of Honour at Windsor Castle.
Ms Bruni-Sarkozy curtsied when she met the Queen - a skill she had reportedly been practising.
Criticised by some in France for his showy style, Mr Sarkozy was treated to some British opulence with a short journey in a gilt carriage through Windsor, accompanied by the Queen.
Once the French president and entourage had arrived in Windsor, a ceremonial parade was held through the town. It is the first full state visit by a French president for 12 years.
Arriving at Heathrow on Wednesday, the couple were met on the red carpet by Prince Charles, who kissed the hand of Ms Bruni-Sarkozy.