There are a number of issues.

First, the braces {...} in your sed expression are not matched by anything in the input. In a sed Basic Regular Expression, braces are literal, while in an Extended Regular Expression they surround a quantifier of the form {n,m}. They are never used for grouping.

Second, your color sequence is malformed - the opening needs to be 033[0;34m rather than 033[0;34

Third, the backslash character is special in sed - in particular, a backslash followed by a decimal digit on the RHS of a substitution is a backreference to a capture group; at least in GNU sed, 0 refers to the whole captured LHS equivalent to the special replacement token & so for example

$ echo foo | sed 's/foo/033bar/'

foo33bar

To pass a literal to the outer echo -e you'd need inside the sed replacement string.

Finally, is also special to the shell, so inside "soft" double quotes needs an additional backslash. So either:

echo -e "$(echo "This is an uncolored text" | 

  sed "s/This is an uncolored text/This is an 33[0;34muncolored text33[0m/")"

or (replacing the inner double quotes with 'strong' single quotes):

echo -e "$(echo "This is an uncolored text" | 

  sed 's/This is an uncolored text/This is an 033[0;34muncolored text033[0m/')"

Note that you don't need the g modifier to make a single replacement per line.

See also What characters do I need to escape when using sed in a sh script?