  The double-copy construction for form factors was reported in our previous
work, in which a novel mechanism of turning spurious poles in Yang-Mills theory
into physical poles in gravity is observed. This paper is the first of a series
of two papers providing the details as well as various generalizations on the
double-copy construction of tree-level form factors. In this paper, we
establish the generic formalism by focusing on the form factor of ${\rm
tr}(\phi^2)$ in the Yang-Mills-scalar theory. A thorough discussion is given on
the emergence of the "spurious"-type poles and various related properties. We
also discuss two generalizations: the Higgs amplitudes in QCD, and the ${\rm
tr}(\phi^2)$ form factors with multiple external scalar states.
