The 'Fight Blue with Blue' campaign aims to bring a positive Dutch mindset to UK consumers.
It is based on research that shows the Netherlands is the fifth-happiest country in the world, with the UK ranked 15th.
Frank's remit in the brief includes management of PR and experiential rollout surrounding the campaign, with Influence Digital leading the digital execution, content creation, media buying and influencer management.
KLM is the oldest airline to operate under its original name and last year celebrated its centenary.
Benedicte Duval, general manager for Air France-KLM in the UK and Ireland, said: "We're thrilled to be working with both agencies to bring the joy of the Netherlands to the UK this January.
"Influence Digital came to us with the campaign concept last year and we fell in love with it. We then brought Frank into the fold and the concept was born! We can't wait to make the idea a reality and spread much-needed cheer across the UK."
Frank founder and managing partner Andrew Bloch said the agency admired "the smart and creatively topical work KLM has delivered for years" and was "hugely honoured to be adding the brand to our client portfolio".
He added: "KLM leads the charge when it comes to regional connectivity, customer-centricity and sustainability, and we look forward to working hand-in-hand to bring this to life in the forthcoming brand campaign."
Influence Digital, which specialises in digital and social-media marketing, has worked with KLM for several years.
"The 'Fight Blue with Blue' campaign very much conveys the friendly and caring nature of KLM and brings to life those core brand values at a time of the year when the UK needs a boost. We're really excited about activating 'Fight Blue with Blue' and spreading Dutch joy to the nation," said Influence Digital managing director Carlos Rodrigues.