She also "concedes" that their firstborn looks more like him than her.
On Instagram, the 35-year-old mom writes: "Each time I see a precious moment between you and our daughter, my heart is filled with so much love, to the point of it bringing tears to my eyes (as you have seen the past few months).
"You are such an amazing father to our Dahlia Amélie.
"From early morning smiles, nappy changes, burping sessions, cheeky monster faces and sarap cuddles—being a father has come so naturally to you.
"We are so lucky to have you in our lives.
"And because it is Father’s Day, I’ll finally concede [tongue out emoji]... our little girl is a little Erwanita.
"She looks so much like her papa...the cutest little bb girl..."
Anne also reveals that one of her pinaglihian when she was pregnant was Erwan's face.
"I guess lihi is real after all," the Kapamilya star says.
"Je t'aime Mon amour (I love you my dear).
"Happy 1st Father’s Day."
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Anne and Erwann tied the knot on November 12, 2017, in Thurlby Domain, Queenstown, New Zealand.
The celebrity couple welcomed Baby Dahlia Amélie on March 2, in Melbourne, Australia.