Urgent advice needed re. a one-day visit in Paris - 24 October 2016

I am a Polish-British Canadian (male, nearly 60) who spent a long time in Belfast, Northern Ireland, where I went to Queen's and then lived for many years. I am now back in Europe, and will be traveling to Paris soon (24 October), where I will have one day to see... everything.  I have a few specific questions about Paris - if anyone would be willing to answer.
And in particular, I have one issue/problem:
I will be there with my adopted daughter (20, currently studying in Cambridge), and we will be arriving after a sleepless night (due to a very early flight), and then will be rushing around Paris to see things. I expect there will come a moment, when we will be just... exhausted - so would need a place to sit down and even close our eyes for an hour or two, in some quiet spot.  But were to find such a place?!
No point paying for a hotel for that.  If anyone will be willing - for a fee - to give us a cup of tea and let us sit in peace for a short time in their place, that would be greatly appreciated.
Thank you!
Wojtek (pronounced Voytek - it is a Polish name)

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