Did I really write Maré ?
Yes, Marais was what I meant, not far from the Centre Pompidou and Les Halles, too (what happened there - have you been there by any chance, scepticalscribe? They were doing a major urban 'renewal' there). It's worth discovering it by foot and probably without a pre-planned route (that's how I experience (foreign) cities whenever I can).
If you want to go romantic, take a boat trip on the Seine where you visit the nine (?) brigdes of Paris after dinner. It's sth. called with Pont Neuf if I remember correctly.
Yes, I stayed in a small hotel just behind the Pompidou Centre, so I walked the entire area, (slowly), as that is how I, too, like to experience foreign cities, especially cities with ancient, compelling, historic centres. Usually, I take a good map with me, but I don't always follow it (unless I have a specific destination in mind). The map is usually to orientate myself subsequently when I wander off in a different direction.
So, yes, I did a lot of walking (and stopping for coffee when flagging). Actually, I rather liked it, the 'urban renewal' you mentioned, the French usually manage to incorporate a degree of modernity without offering outrageous insults to the past. Thus, you have this extraordinary city, quite beautiful in parts, where the ancient and the modern co-exist quite happily.
One other thing struck me, though, as I hadn't been in Paris for a quarter of a century (it is shocking to write such a thing - a quarter of a century!), and it is this. When I first visited Paris as a school kid (learning French) and later, on a few occasions as a student, and when I first started teaching, I remember it as a working capital, a bureaucratic, business, and cultural capital - with an amazing historic and artistic centre - of a major European power. Now, it has become a heritage centre; Paris makes its living out of its history, culture and gastronomy - I did not get the sense of a thriving, bustling, powerful commercial and political urban centre (the way you do in, say, London, or Brussels or Frankfurt and Berlin.)
This is also reflected in the decline in the use of the French language; once, they revelled in their culture, and French used to be the main working language of the EU, and of diplomacy. Not any longer; even in Paris, most of the staff in cafes, and restaurants speak perfectly good English - and, while they are delighted if you try to speak French to them - you do not get glared at (as you would have years ago) when speaking English. In other words, from what I could see, they have lost the cultural war, and the language war, and are content to live off their heritage rather than add to it, and expend energy on trying to persuade Europe of the merits (which are many) of their way of life.