To build on George's answer, you could parse the message into tokens then build the message from the tokens.
If the template string was much larger and there are more tokens, this would be a tad more efficient as you are not rebuilding the entire message for each token replacement. Also, the generation of the tokens could be moved out into a Singleton so it is only done once.
// Define name/value pairs to be replaced.
var replacements = new Dictionary<string, string>();
replacements.Add("<Name>", client.FullName);
replacements.Add("<EventDate>", event.EventDate.ToString());
string s = "Dear <Name>, your booking is confirmed for the <EventDate>";
// Parse the message into an array of tokens
Regex regex = new Regex("(<[^>]+>)");
string[] tokens = regex.Split(s);
// Re-build the new message from the tokens
var sb = new StringBuilder();
foreach (string token in tokens)
sb.Append(replacements.ContainsKey(token) ? replacements[token] : token);
s = sb.ToString();