The Financial Conduct Authority (FCA) said advisers at AXA Wealth Services sold £440m of investment products without clearly explaining the risks involved or adequately checking if products were suitable.
AXA had 201 sales advisers operating out of branches of Clydesdale and Yorkshire banks as well as 23 at the separate West Bromwich Building Society.
Glasgow-based Clydesdale transferred its financial planning service to AXA in 2009 in a move that saw nearly 80 jobs cut.
AXA said in April this year it was closing its service in Clydesdale branches for reasons unrelated to the regulator's probe.
Tracey McDermott, FCA director of enforcement, said: "AXA fell short of its responsibilities to its customers, many of whom were elderly, retired and financially inexperienced.
"Its failures resulted in an unacceptable risk of AXA selling products which were unsuitable for its customers."
The FCA found that AXA sold 37,000 products, such as stocks-and-shares individual savings accounts (ISAs) and investment bonds, between September 2010 and April 2012, to 26,000 customers.
Sales advisers on basic salaries of £23,000 to £30,000 could take home as much as £75,000 if they sold enough products.
The FCA found that in 2011, 83% of sales advisers received sales bonus payments, with the average commission paid out reaching nearly £9000 each.
Until January 2011, advisers could still receive full bonuses, even if as much as 40% of sales were found by AXA compliance staff to be unsuitable for investors.
The FCA said it was fortunate that customer losses had been minimal due to a rally in stock markets over the last three years.
An AXA spokesman said: "We take regulatory compliance very seriously and regret that the customer advice provided by the bancassurance division between September 2010 and April 2012 did not meet the high standards expected by the FCA."
The authority will contact affected customers and compensate those who have suffered losses as a result of mis-selling and offer those sold inappropriate products the option to switch or end their investments.
A spokesman for Clydesdale said: "The regulator has been clear that there are no findings against our business. AXA have agreed a review process with the regulator to support any impacted customers."