Entry into the Grand Palais is free of charge and when you see the building's exterior you'll…read moreimmediately decide that you must go inside. It's stunning, though you'll soon realize that the part you most wanted to see - the glass enclosed space - might not be open to you.
Visiting in May, the glass-domed space was locked tight, opened only for special shows and events. I've looked at the calendar now, in June, and see that they open it for many summer activities and were I there now I'd certainly try to get tickets for one of those events.
Otherwise? This is still a worthy investment of time, not just to look around and peer into the glass-domed space, but to view the exhibits (individually priced, tickets available at the door). I noticed 3 special exhibits during my visit and paid for entry to 2 (Matisse and Nan Golden). Based on this experience, I'd recommend paying for entry to the exhibits of artists you're least familiar with under the assumption that they'll be less crowded. The Matissse exhibit was crowded enough to render the experience almost unpleasant. The Nan Golden show? Perfect.
Though I'd recommend paying to see some exhibits, even if all you do is enter to walk around and explore the space you'll be nicely rewarded. The Grand Palais has some pleasant, quiet seating areas inside and the space is lovely.