If she's a good enough girlfriend to take to Paris, then she should also be open to getting her own Chase Hyatt card! Then you have four nights at the Park Hyatt and can add two more with Sapphire points transferred to Hyatt.

In terms of your question about better rates with packages - booking packages is often better since the airlines wholesale the tickets to their package division. Prices can actually be amazing for Business Class tickets where the package price is less than just the two tickets!

Finally, there is some Coach availability on Air Canada from Boston with a stop in Canada - think the dates I saw were Aug 8-15. You can get one ticket on miles and one for cash. That would mean then entire trip for the price of one ticket + Air Canada fees. I also found Air France Coach availability for similar dates. Both are AMEX transfer partners.

Paris is my favorite city and the Park Hyatt is easily my favorite hotel. Looks like you're going. Enjoy!