Hollande arrived here this afternoon as he began his three-day visit to India during which, among other things, he will be attending the Republic Day function as Chief Guest.
Modi reached Chandigarh -- the city designed by French architect Le Corbusier -- around 80 minutes after Hollande's arrival here at 1 PM.
Upon meeting, the two leaders shook hands and hugged each other even as traditional Punjabi folk dance, 'Giddha', was performed to welcome them.
The French President took keen interest in viewing the artefacts made from household and industrial waste and other material and also sought details about the artworks, which feature animal and human sculptures made out of bangles, ceramic tiles, bathroom fittings, etc.
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On a bright and cheerful morning, those visiting Rock Garden along with the two leaders took photos and selfies on their mobile phones even as Modi and Hollande went around the place.
A tight security cover was in place with armed personnel keeping a close vigil as the high-profile visitors spent about 20 minutes at the Rock Garden.
The prime minister wore a sky-blue jacket with a brown- coloured shawl while Hollande was in a dark suit.
After visiting the Rock Garden, the duo proceeded to the adjacent Capitol Complex, which includes the 'Open Hand Monument' besides the Secretariats, High Court and Legislative Assembly of Punjab and Haryana, designed by Le Corbusier.
Elaborate security has been put in place in the joint capital of Punjab and Haryana, which is hosting a foreign president for the first time. Apart from personnel from Punjab, Haryana and the Union Territory of Chandigarh, central paramilitary forces, including ITBP, have also been deployed.
At the Capitol Complex, Modi and Hollande were welcomed by Punjabi folk performers.
Modi was seen chatting with Hollande even as the two took a walk in the complex that is located in the foothills of the Shivaliks.
The two leaders posed for photographs with the Legislature Complex in the background and warmly shook hands as they posed for photographs.
From there, the two left for the Government Museum and Art Gallery.
Late Nek Chand Saini was the creator of the iconic Rock Garden, that has amazed people for decades with his unique sculptures made from waste. 90-year-old Chand died in June last year following a cardiac arrest.
Inaugurated in 1976, Rock Garden comprises several thousand sculptures set in large mosaic courtyards linked by walled paths and deep gorges.
Chand's creation also combines huge buildings with a series of inter-linking waterfalls.
More than 2.5 lakh people from India and abroad visit it every year with the annual revenue generated from ticket sales coming to around Rs 1.8 crore.
Rock Garden became immensely popular in the 80s with Chand receiving the Padma Shri in 1983 and a sculpture from the site appearing on an Indian postage stamp.
It is seen as symbolising the spirit of exaltation, power and permanence which was experienced by Indians upon acquiring self-government after a long, bitter struggle for freedom.
Following the visit to Capitol Complex, the two leaders went to the Government Museum and Art Gallery, where they were welcomed by Bhangra dancers.
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In a tweet later in evening, Prime Minister Narendra Modi said it was a "delight" to take the French President around parts of Chandigarh.
The Prime Minister said in his tweet, "It has been a delight to take President @fhollande around parts of Chandigarh, a city associated with noted architect Le Corbusier."
On his visit to the museum, Modi said in a tweet, "Viewed displays of archaeological findings from foothills of the Himalayas with President @fhollande at the Government Museum & Art Gallery."
In another tweet, he said, "The displays are result of years of hardwork between Indian & French researchers. Such exchanges are a special aspect of India-French ties.