When I say "hearts," I mean he really, truly loved it. While in Paris for five years in the late 1780s, he wrote that he was "violently smitten with the hotel de Salm". Violently smitten! What a wonderful expression.
So what's the deal with the this place? I know I've walked by it before and never noticed it.
Well, the Hôtel de Salm is located in the 7th arrondissement just next to the Musée d'Orsay. If you're standing facing the Musée d'Orsay, the Hôtel de Salm is the next building to the right, just past rue de la Légion d'Honneur.
A fellow history lover told me the story about it just before my last trip to Paris and I made it a mission to see it. It's one of those wonderful stories that's hiding in plain sight.
Pierre Rousseau originally designed and built it between 1782 and 1787 for Frederick III, Fürst of Salm-Kyrburg. Since the 7th has long been home to nobility, it's fitting that he was a German Prince. I imagine that even in the 1780s, a piece of property on the Seine was worth a pretty penny--err--denier.
During the construction, apparently Jefferson would spend hours watching the building process. Here's how it looked in 1786, the way Jefferson would have seen it.
Americans or American history lovers might see something familiar. Here is the Jefferson statue's current view.
Do you see it? Yup! Monticello!
Jefferson loved architecture. He once said, "Architecture is my delight, and putting up, and pulling down, one of my favorite amusements."  That's just what he did with Monticello.
Jefferson's original design for Monticello took inspiration from renowned architect Andrea Palladio's Italian villas. He was happy with it for a while.
But in 1784, he went to Paris for 5 years as Minister to France, succeeding Benjamin Franklin in 1785. He fell in love not only with the Hôtel de Salm but with Paris and France in general. Of the French he wrote, "I do love this people with all my heart." 
So, when he returned home, he took his newfound inspiration and redesigned/Salm-ified Monticello.
On July 4 in 2006, Jefferson's statue was unveiled across the street from the Hôtel de Salm as a gift from the Florence Gould Foundation and Alec and Guy Wildenstein. The University of Virginia alumni in Paris, the Thomas Jefferson Foundation, and Guy Wildenstein worked for over a decade to get the statue installed. 
In Jefferson's hands are a quill and his design ideas for Monticello, based, of course, on the Hôtel de Salm.
As for the Hôtel de Salm, it is now also known as the Palais de la Légion d'Honneur. Napoleon established the Légion d'Honneur as the highest decoration in France. You can go visit the National Museum of the Legion of Honor and the Orders of Knighthood there. It is open on Wednesdays through Sundays between 1 pm and 6 pm. The entrance is at 2 rue de la Légion d'Honneur. Its free (!) and they provide an audio guide.
I didn't know it was a museum until today, so I guess I'll have to go back to Paris at some point. Oh, darn.
Frankly, it was a rush for me to finally stumble on the statue and building while we were there. In my head I was going "OMG! It's Thomas Jefferson!" I guess that's just my history nerd shining through, though.
A Quick Note About Sources and Further Reading
There's lot of in-depth information on Monticello's official website for those interested in more details.
The University of Virginia has a bit more information about statue's installation here.
I also found this September 1987 article from the New York Times travel section on Jefferson's travel experience in France fascinating. Did you know he wrote a travel guide entitled, Hints to Americans Travelling in Europe?
As I read, the article mentioned a slave, James Hemings, traveling with Jefferson. It's was eerie to see that name after now knowing about Sally Hemings. Well, I did a little quick digging, and it turns out James was Sally's brother and she actually ended up in Paris as well. I know that's not a happy note to end on, but it may be interesting to some.