Navigo 2019 Information
 

Haven't been to Paris in years, regrettably. See to recall buying things like Formule 1, Carte Hebdomadaire, Coupon Orange, etc.

I'll be arriving on a Friday and staying through Tuesday.

If I buy Navigo, will I have to pay again on Monday or did they do away with that rule and run a week as seven days from purchase?

Otherwise, is the best bet a carnet? It seems like the Paris Visite is not a great deal.

Unfortunately the Navigo weekly pass is still just that, a pass based on days of the week and not a 7 day pass. It runs Monday-Sunday, so likely not a good option for you. One benefit is that it has been expanded to cover the entire Paris area, zones 1-5, for only €22.80. That includes RER and Roissybus service to CDG. The physical card is €5, and lasts for 10 years.

https://parisbytrain.com/paris-train-metro-week-pass-navigo-decouverte/amp/

Correct, it is still a Monday-Sunday subscription for the weekly.

In addition, I believe you can only buy the weekly subscription thru Thurs of the week (inclusive), so if you arrive on a Friday, you can only buy for the upcoming week.

It is possible to buy a daily Navigo subscription if you already have a pass. Otherwise probably a paper ticket is the better option.

The Paris Visite is not generally a good value. Any weekly Navigo fare purchased after Thursday of the current week, will not be usable before the following Monday.

Probably your only option would be a group of 10 tickets T+ for 14.90€. Individual tickets T+ cost 1.90€ or 2€ when purchased directly from a bus driver.

We used the carnets. I can confirm the Monday to Sunday rule for the weekly Navigo as posted by several here.

However, on my last Metro trip, I noticed something about a daily Navigo pass. Is that worth it?

Depends. For a single day, yes.

But for multiple days, the Paris Visite ticket then gets discounted, versus a fixed daily fare with the Navigo, so it's better for 2+ days within centre Paris to get the paper ticket.

To compare the tarifs :
Forfait Navigo Jour - Tarifs - Navigo

https://www.ratp.fr/titres-et-tarifs...t-paris-visite