Brown, 75, led Scotland to Euro 96 and the 1998 World Cup as manager and believes Wales can shine in France.
Next summer's finals will be Wales' first appearance at a major tournament since 1958.
"When you see the Welsh team play, they're excellent. I think they've got a very good chance," said Brown.
"They won't surprise me, but they could surprise a few folk."
Wales will not face the Republic of Ireland, who reached the finals as ex-Wrexham striker Jon Walters scored both their goals in the victory over Bosnia-Herzegovina on Monday night.
The Republic are set to join Wales and Northern Ireland in pot four for the Championship draw.
Assistant manager Osian Roberts says Brown's insights and advice have been valuable.
"Craig Brown has been a great help to us and Chris [Wales boss Coleman] knows him very well," Roberts said.
"I was out with him at a conference in Russia last week. We had a couple of hours going through all the details, which I've brought back and shared.
"There's people with a wealth of experience we can tap into, so we're doing that.
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"It gives us a great insight into how to go about it because it's a learning curve for us."
The draw for the Euro 2016 pools is scheduled to take place in Paris on 12 December, with Wales among the lowest seeds.
Coleman's men hope to finalise their training base for next summer's finals in France before the end of 2015.
Euro 2016 matches will be played in Paris, Bordeaux, Lens, Lille, Lyon, Marseille, Nice, Saint-Denis and Toulouse.
An under-strength Wales side lost their first pre-Euro 2016 friendly to the Netherlands 3-2 in Cardiff on Friday.
Wales' next friendly window will be in March and the ramifications of the draw will be considered before a list of suitable opponents is drawn up.

Net profit for the quarter rose to 28.86bn rupees ($481m) from 23.74bn rupees a year earlier.
The figure beat analysts' expectations and shares in the company jumped 4% on the Bombay Stock Exchange.
The IT outsourcing company recently appointed technology veteran Vishal Sikka as its chief executive.
A former board member at SAP, Mr Sikka is the first outsider to run Infosys.
Business has been improving for the Indian firm after a difficult period of lower client spending.
The company reported revenue of $2.1bn in the quarter, and maintained its forecast for full-year revenue growth at 7-9% in dollar terms.
Infosys currently employs 160,000 people, but it admitted that it had been losing employees to competitors and was taking steps to address this.
"Employee attrition rates are worrisome and we are implementing various initiatives to retain good talent", said chief operating officer U. B. Pravin Rao.
Infosys is seen as a key indicator of the health of India's IT outsourcing industry, which is valued at more than $100bn.

Police said the 20-year-old victim was hit by a silver Vauxhall Vectra at 04:30 BST as he crossed Anderson Street, in South Shields.
He died at the scene. The accident happened near the junction with Beach Road, police said.
Northumbria Police said a 20-year-old man was later arrested on suspicion of causing death by dangerous driving.
He remains in police custody.
Wales have sought the advice of former Scotland manager Craig Brown to help their preparations for the Euro 2016 Championship in France.
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Infosys, India's second-largest software firm, has reported a 21% increase in quarterly profit and maintained its revenue growth forecast.
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A man died after being struck in a suspected hit-and-run crash in South Tyneside.