While it is claimed here and there that Picard name is inspired by Auguste Piccard, the first man who saw the Earth’s curvature, and his family of balloonists and bathyscaphists, is this actually mentioned in the series? Wikipedia does not have a precise reference.
According to Wikipedia Gene Roddenberry created the name Jean-Luc Picard for one or both of the Piccard brothers. However it is not related at all to the fictional ancestry of the character Jean-Luc Picard.
In the family photo album which Picard has in both Generations and Nemesis the opening cover shows the "beginning" of the Picard family line as Madame de La Barre and Francoise de Picard.
The caption on the photo reads:
The founders of the family, Madame de La Barre and Francoise de Picard
In Generations Picard speaks briefly about his family's heritage, mentioning the Picard who was at Trafalgar and in the first Martian colony.
Memory-Alpha says that Picard claimed he was able to trace his family's roots back to the time of Charlemagne in the 8th century, which is well before the time of Auguste Piccard. Given the consistency of the single 'c' in Picard, is it extremely unlikely he would be related to people with a deviation in the name.
It's unlikely that such a reference would exist in the series - Picard is a last name, not a given name. Jean-Luc has the last name of 'Picard' because his father did. His father had that last name because his father did, and so on. Thus, Picard would never say, "I was named after Auguste Piccard". The difference in spelling between Jean-Luc's name and Auguste's name makes a direct ancestry less likely, as well.
In general, excepting those who do so through legal channels or during immigration, people don't choose their last names. Most people don't even know the background of their last name, though they may be aware of ancestors who were important or well-known.
It's entirely possible that the writers and producers chose the name 'Picard' as a reference to the gentleman you mention. If so, however, I do not recall Picard naming him as an ancestor during the show, not do I recall any specific interview where the shows staff or producers said as much.
It could be possible. For example, my last name is Perlich. I'm a 3rd generation American. When my great great grandfather and his family immigrated into the US, the last name was originally Berlich. For some reason it was changed (possibly a misspelling by immigration authorities at Ellis Island). Since Auguste Piccard is from the early 20th century, and Jean-Luc is from the 24th, it's entirely possible that the last name was slightly changed. It's also possible, in the fictional sense, that Auguste Piccard could be related to the ancestrial Picard, but that the last name was changed to Piccard for some reason or another, and then corrected prior to Jean-Luc. I know, a far fetch, but this is fiction that we're talking about.