Four-month-old Ted visits Wales twice a month to see his grandparents in Carmarthenshire and the TV star hopes he will be brought up to be bilingual.
He will be heading back again with his mother for the Champions League final.
Ms Jones will present a One Show special from Cardiff on Friday, the eve of the men's match.
The 40-year-old, who returned from maternity leave to the BBC One show part-time in April, said she was excited to be in the city for an event of such magnitude.
"Working in Cardiff is a dream for me - the city will be buzzing," she said.
"That's one of the best things about Cardiff - when we're hosting events like this the city comes alive."
The Ammanford-born star lived in Cardiff for years and said it still felt like her home, adding she missed it "lots and lots".
As a Welsh speaker herself, Ms Jones said she hoped to pass on the language to her son and had spoken about it with her husband, Charlie Thomson, who is from New Zealand.
"It's hard in London but I will definitely speak Welsh to him and Charlie knows the odd word," she said.
"There's a Welsh primary school here [in London]  and I would love him to go there.
"It's part of my heritage and is a big part of my identity. It's a big thing for me for Ted to experience it - I really benefitted from being bilingual."
She admitted it had been "tough" going back to work with such a young baby, although she joked that The One Show was "a break" from the "really hard job of motherhood".
"Going back part-time was the right thing to do - it's good for Ted to know women work," she added.
"And actually it comes down to necessity, there's no choice, I have to work."
She said she was looking forward to showing The One Show team "Cardiff at its best" and will even host a tour of the city for the programme, which she will be co-hosting with Patrick Kielty and Jason Mohammad from Cardiff Bay.
Top of her must-see sights?
"It's got to be Cardiff Castle," she said.
"There's a lot of history for us there as we got married there. It has beautiful grounds for a picnic and has lots of interesting history. And the view from the top is spectacular.
"I'm a bit out of the loop with where to go for a night out having had a baby but you can't go wrong with Cardiff Bay on a sunny evening."
It is, perhaps, where she will be heading after finishing her live broadcast for The One Show on Friday.
"I'm having my first night out with my friends since having the baby afterwards," she added.
"It's going to be amazing. I know Cardiff will do us proud."
The One Show - Live in Cardiff is on BBC One at 19:00 BST on Friday, 2 June
The One Show presenter Alex Jones has spoken of her wish to teach her baby son to speak Welsh but admits it might be a struggle while living in London.