"Et" pour commencer une phrase

Jean, 

The expression is ‘ et puis ‘ - this is accepted and colloquial use. Here it is in an informal conversation between friends. 

 https://www.larousse.fr/dictionnaires/francais/puis/65014

 https://www.wordreference.com/fren/et%20puis 

Even though English and French grammar doesn't need to have the same grammatical rules, it is also acceptable to start sentences in English with ‘ and ‘, ‘ but ‘ etc, contrary to what we may have been taught in our early school days.

 https://www.scribophile.com/academy/starting-a-sentence-with-and

https://writegroup.io/grammar-tip-why-its-smart-to-start-a-sentence-with-a-conjunction/

https://academic.oup.com/book/55355/chapter-abstract/430402906?redirected

From=fulltext (published by Oxford Academic Press)

“ Writers have opened sentences with and since the Old English period. Chaucer did it. So did Malory, Shakespeare, the translators of the King James Version of the Bible, and many others. And authors have been starting sentences with but since the Middle Ages. Chaucer did that a lot, and Shakespeare and Milton did it, too.1 Even the early grammarians who prescribed many of the weird usage rules in English had no problem with starting sentences with but. In the nineteenth century, though, some schoolteachers opposed starting sentences with and or but, possibly because young students did that too often. Then teachers went overboard, banning the practice altogether.2 Today, most language experts and stylists agree that it’s fine to open sentences that way. In fact, The Chicago Manual of Style points out that up to ten percent of the sentences in first-rate writing begin with conjunctions such as and, but, or so.3 Starting with but can be stylistically powerful. It packs a punch that the more formal-sounding word however doesn’t. Just don’t do it too often.”