As an expatriate Frenchman who learned English as an adult, I am a big believer in giving kids the advantage of bilingualism. If you’re raising Lucy to speak two languages, start speaking your maternal tongue to her as early as the newborn stage. This will help you communicate with her in the most spontaneous and natural way. Later, you’ll be happy she can chat with grandma and grandpa in their own language. Don’t worry about the English; she’ll pick it up when she starts socializing.
Switching from one language to another may be a little confusing for Lucy, but most bilingual kids acquire both tongues simultaneously at the same point that their monolingual peers are mastering just one. For late talkers, this exercise may delay language acquisition a little, but stick with it! The benefit of having two languages outweighs the disadvantage of lagging a few weeks before talking. In either case, be careful not to mix languages within one sentence or conversation, because this may confuse someone who’s just starting to understand them both.
I wish I had practiced what I preach with my own kids. I only spoke French with the first one, and she’s managed to keep some of it. By the time the two youngest showed up, I’d become lazy. Now I pay Veronique (their charming French teacher) thirty dollars an hour each week to instill in them the rudiments of Voltaire’s tongue.