The injury happened at Parsonage Hotel and Spa at Escrick, York Magistrates Court heard.
Smith and the company, both of Lords Moor Lane, Strensall, each pleaded guilty to an offence under health and safety regulations committed on or before November 8, 2021.
The charge says they didn’t adhere to health and safety policies and risk assessments, didn’t sufficently protect customers from harm on the premises and didn’t train staff effectively.
The company was fined £40,000 and ordered to pay a £190 victim surcharge and £10,524.44 towards the prosecution’s costs.
Smith was fined £6,422 and ordered to pay a £190 victim surcharge and £1,739.70 towards the prosecution’s costs.
Both defendants were prosecuted by Selby District Council.
Its executive member for health and culture, Cllr Tim Grogan, said: “This is another successful prosecution by our environmental health team who work diligently to keep residents of the Selby district safe.
“They’ve worked hard to secure this result and the court’s decision sends a clear message that the safety of customers visiting establishments in our district is a high priority.”