Brand, 34, has joined Perry, 25, at fashion shows and parties for Paris' fashion week, taken eerie strolls at dusk around a famous cemetery and been spotted partaking in demure hand-holding.
"They arrived at John Galliano hand-in-hand," one attendee tells PEOPLE. "They seem very much like the real thing."
Contacted by PEOPLE Thursday about the burgeoning relationship, Brand's rep had no comment. But British newspaper Web sites, like The Sun and Daily Mail, express no doubt that the couple are loved-up in the French capital.
A 'Twilight' Remake?The latest shots at Wednesday night's John Galliano show in Paris reveal Perry in a pink gown being attentively chaperoned by Brand. Earlier, that day, they had left their hotel in the Place Vendôme and drove across town to Pére Lachaise cemetery, which houses the remains of rocker Jim Morrison, playwright Oscar Wilde and chanteuse Edith Piaf.
"It was getting darker in the late afternoon and I'm taking pictures of this couple with long black hair, both of them, and dressed in black walking around the tombs in a cemetery," one photographer told PEOPLE. "I asked myself, "Are they planning on remaking Twilight?"
Thailand and LondonPerry later wrote on Twitter of her time at the Galliano show at Halle Freyssinet, "Oh my, Galliano was by far the best. It was a dark sexy dream of beautiful mental sparkling women, I can relate to that, the mental part!"
Using his "Rusty Rockets" alias, Brand tweeted to his followers Wednesday: "I'm in 'Gay Paris' – I swear as an Englishman that by the time I leave tomorrow it'll be known as 'Hetero Paris.' Or at least Bi Paris.' X"
The break in Paris follows their reported weeklong break in Thailand together and, last weekend, they were spotted strolling in London. And on Saturday, Perry was spotted doing the walk of shame from Brand's house in London.
The couple appear alongside each other briefly as he reprises his Forgetting Sarah Marshall character Aldous Snow in next year's Get Him to the Greek.